Forms of Lock-Up Agreement

Exhibit 10.2

Form of Lock-Up Agreement - Vital Therapies Officers

Lock-Up Agreement

April    , 2019

Immunic AG

Am Klopferspitz 19

82152 Planegg-Martinsried

Germany

Ladies and Gentlemen:

The undersigned (the “Lock-Up Participant”) is entering into this agreement in connection with that certain Exchange Agreement dated as of January 6, 2019 (the “Exchange Agreement”) among Vital Therapies, Inc, a Delaware corporation (“Vital”), Immunic AG (“Immunic”) and the shareholders of Immunic, whereby the shareholders of Immunic will contribute, transfer, assign and deliver all of the Common Shares and Preferred Shares of Immunic (collectively, the “Immunic Shares”) owned by them, and all of their rights with respect to such Immunic Shares, to Vital in exchange for shares of the common stock, par value $0.0001 per share, of Vital (the “Vital Common Stock”), with the result of Immunic becoming a wholly-owned subsidiary of Vital (the “Transaction”) and the Lock-Up Participant, as a holder of shares of Vital Common Stock and/or shares of Vital Common Stock issuable pursuant to the exercise of Vital Options and/or the vesting of Vital Severance RSUs. Capitalized terms used but not otherwise defined herein shall have the respective meanings ascribed to such terms in the Exchange Agreement.

The Lock-Up Participant hereby agrees that, without the prior written consent of Vital (or, from and after the Effective Time, Immunic, Inc.), the Lock-Up Participant will not, during the period commencing on the date hereof and ending 180 days after the date of the Closing (the “Lock-Up Period”), (1) lend, offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, or otherwise transfer or dispose of, directly or indirectly, any shares of Vital Common Stock or any securities convertible into or exercisable or exchangeable for Vital Common Stock (including, without limitation, Vital Common Stock or such other securities which may be deemed to be beneficially owned by the Lock-Up Participant in accordance with the rules and regulations of the SEC and securities which may be issued upon exercise of a stock option or warrant), or publicly disclose the intention to make any offer, sale, pledge or disposition; (2) enter into any swap or other agreement that transfers, in whole or in part, any of the economic consequences of ownership of Vital Common Stock or such other securities, whether any such transaction described in clause (1) or (2) above is to be settled by delivery of Vital Common Stock or such other securities, in cash or otherwise or (3) make any demand for or exercise any right with respect to the registration of any shares of Vital Common Stock or any security convertible into or exercisable or exchangeable for Vital Common Stock, in each case for purposes of clause (1) or (2) above other than (A) transfers of shares of Vital Common Stock or such other securities as a bona fide gift or gifts, (B) distributions of shares of Vital Common Stock or such other securities to current or former, direct or indirect, members, stockholders, limited partners, subsidiaries or affiliates (as defined in Rule 405 promulgated under the Securities Act) of the Lock-Up Participant or to any investment fund or other entity that controls or manages the Lock-Up Participant (including, for the avoidance of doubt, a fund managed by the same manager or managing member or general partner or management company or by an entity controlling, controlled by, or under common control with such manager or managing member or general partner or management company as the Lock-Up Participant or who shares a common investment advisor with the Lock-Up Participant) in a transaction not involving a disposition for value, (C) sales or other dispositions or arrangements involving shares of Vital Common Stock acquired in the open market after the Closing, (D) a bona fide third party tender offer, merger, consolidation or other similar transaction made to all holders of Vital Common Stock involving a change of control of Vital following the Closing (including, without limitation, entering into any lock-up,

voting or similar agreement pursuant to which the Lock-Up Participant may agree to transfer, sell, tender or otherwise dispose of Vital Common Stock or such other securities in connection with any such transaction, or vote any Vital Common Stock in favor of any such transaction), or (E) transfers of shares of Vital Common Stock owned by the Lock-Up Participant in a private transaction; provided that in the event that the tender offer, merger, consolidation or other such transaction is not completed, the Vital Common Stock owned by the Lock-Up Participant shall remain subject to the restrictions contained in this Lock-Up Agreement, provided, that in the case of any transfer or distribution pursuant to clause (A) or (B), each donee, distributee or transferee shall execute and deliver to Vital a lock-up letter in the form of this Lock-Up Agreement; and provided, further, that in the case of any transfer, distribution, sale or other arrangement pursuant to clause (A), (B), (C) or (E) no filing by any party (donor, donee, transferor or transferee) or the Lock-Up Participant, or any director of Vital affiliated with any party (donor, donee, transferor or transferee) or the Lock-Up Participant, under the Exchange Act, or other public announcement shall be required or shall be made voluntarily in connection with such transfer, distribution, sale or other arrangement, other than a filing on a Form 5 made after the expiration of the Lock-Up Period or any required beneficial ownership filings under Section 13 of the Exchange Act. For purposes of this Lock-Up Agreement, “change of control” shall mean the consummation of any bona fide third party tender offer, merger, consolidation or other similar transaction the result of which is that any “person” (as defined in Section 13 (d) (3) of the Exchange Act) other than Vital, or group of persons other than existing stockholders of Vital, becomes the beneficial owner (as defined in Rules 13d-3 and 13d-5 of the Exchange Act) of fifty percent (50%) of total voting power of the voting stock of Vital.

Notwithstanding any provision herein to the contrary, the restrictions set forth herein shall not apply to any sales of Vital Common Stock by any Lock-Up Participant solely for the purpose of settling Tax expenses in connection with the consummation of the Transaction (it being understood that 50% of the shares of Vital Common Stock issued pursuant to vesting of the Vital Severance RSUs will be freely tradable and not subject to this Lock-Up Agreement).

No provision in this Lock-Up Agreement shall be deemed to restrict or prohibit the exercise, exchange or conversion by the Lock-Up Participant of any securities exercisable or exchangeable for or convertible into Vital Common Stock, as applicable; provided that the Lock-Up Participant does not transfer the Vital Common Stock acquired on such exercise, exchange or conversion during the Lock-Up Period, unless otherwise permitted pursuant to the terms of this Lock-Up Agreement. In addition, no provision herein shall be deemed to restrict or prohibit the entry into a 10b5-1 trading plan at any time (other than the entry into such a plan in such a manner as to cause the sale of any securities subject to this Lock-Up Agreement during the Lock-Up Period).

The Lock-Up Participant understands that this Lock-Up Agreement is irrevocable and shall be binding upon the Lock-Up Participant’s heirs, legal representatives, successors and assigns.

The Lock-Up Participant understands that if the Exchange Agreement (other than the provisions thereof which survive termination) shall terminate or be terminated prior to Closing, then this Lock-Up Agreement shall be void and of no further force or effect.

(Signature Page Follows)

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(Signature Page to Vital Lock-Up Agreement)

Form of Lock-Up Agreement - Vital Therapies Directors

Lock-Up Agreement

April    , 2019

Immunic AG

Am Klopferspitz 19

82152 Planegg-Martinsried

Germany

Ladies and Gentlemen:

The undersigned (the “Lock-Up Participant”) is entering into this agreement in connection with that certain Exchange Agreement dated as of January 6, 2019 (the “Exchange Agreement”) among Vital Therapies, Inc, a Delaware corporation (“Vital”), Immunic AG (“Immunic”) and the shareholders of Immunic, whereby the shareholders of Immunic will contribute, transfer, assign and deliver all of the Common Shares and Preferred Shares of Immunic (collectively, the “Immunic Shares”) owned by them, and all of their rights with respect to such Immunic Shares, to Vital in exchange for shares of the common stock, par value $0.0001 per share, of Vital (the “Vital Common Stock”), with the result of Immunic becoming a wholly-owned subsidiary of Vital (the “Transaction”) and the Lock-Up Participant, as a holder of shares of Vital Common Stock and/or shares of Vital Common Stock issuable pursuant to the exercise of Vital Options and/or the vesting of Vital Severance RSUs. Capitalized terms used but not otherwise defined herein shall have the respective meanings ascribed to such terms in the Exchange Agreement.

The Lock-Up Participant hereby agrees that, without the prior written consent of Vital (or, from and after the Effective Time, Immunic, Inc.), the Lock-Up Participant will not, during the period commencing on the date hereof and ending 180 days after the date of the Closing (the “Lock-Up Period”), (1) lend, offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, or otherwise transfer or dispose of, directly or indirectly, any shares of Vital Common Stock or any securities convertible into or exercisable or exchangeable for Vital Common Stock (including, without limitation, Vital Common Stock or such other securities which may be deemed to be beneficially owned by the Lock-Up Participant in accordance with the rules and regulations of the SEC and securities which may be issued upon exercise of a stock option or warrant), or publicly disclose the intention to make any offer, sale, pledge or disposition; (2) enter into any swap or other agreement that transfers, in whole or in part, any of the economic consequences of ownership of Vital Common Stock or such other securities, whether any such transaction described in clause (1) or (2) above is to be settled by delivery of Vital Common Stock or such other securities, in cash or otherwise or (3) make any demand for or exercise any right with respect to the registration of any shares of Vital Common Stock or any security convertible into or exercisable or exchangeable for Vital Common Stock, in each case for purposes of clause (1) or (2) above other than (A) transfers of shares of Vital Common Stock or such other securities as a bona fide gift or gifts, (B) distributions of shares of Vital Common Stock or such other securities to current or former, direct or indirect, members, stockholders, limited partners, subsidiaries or affiliates (as defined in Rule 405 promulgated under the Securities Act) of the Lock-Up Participant or to any investment fund or other entity that controls or manages the Lock-Up Participant (including, for the avoidance of doubt, a fund managed by the same manager or managing member or general partner or management company or by an entity controlling, controlled by, or under common control with such manager or managing member or general partner or management company as the Lock-Up Participant or who shares a common investment advisor with the Lock-Up Participant) in a transaction not involving a disposition for value, (C) sales or other dispositions or arrangements involving shares of Vital Common Stock acquired in the open market after the Closing, (D) a bona fide third party tender offer, merger, consolidation or other similar transaction made to all holders of Vital Common Stock involving a change of control of Vital following the Closing (including, without limitation, entering into any lock-up,

voting or similar agreement pursuant to which the Lock-Up Participant may agree to transfer, sell, tender or otherwise dispose of Vital Common Stock or such other securities in connection with any such transaction, or vote any Vital Common Stock in favor of any such transaction), or (E) transfers of shares of Vital Common Stock owned by the Lock-Up Participant in a private transaction; provided that in the event that the tender offer, merger, consolidation or other such transaction is not completed, the Vital Common Stock owned by the Lock-Up Participant shall remain subject to the restrictions contained in this Lock-Up Agreement, provided, that in the case of any transfer or distribution pursuant to clause (A) or (B), each donee, distributee or transferee shall execute and deliver to Vital a lock-up letter in the form of this Lock-Up Agreement; and provided, further, that in the case of any transfer, distribution, sale or other arrangement pursuant to clause (A), (B), (C) or (E) no filing by any party (donor, donee, transferor or transferee) or the Lock-Up Participant, or any director of Vital affiliated with any party (donor, donee, transferor or transferee) or the Lock-Up Participant, under the Exchange Act, or other public announcement shall be required or shall be made voluntarily in connection with such transfer, distribution, sale or other arrangement, other than a filing on a Form 5 made after the expiration of the Lock-Up Period or any required beneficial ownership filings under Section 13 of the Exchange Act. For purposes of this Lock-Up Agreement, “change of control” shall mean the consummation of any bona fide third party tender offer, merger, consolidation or other similar transaction the result of which is that any “person” (as defined in Section 13 (d) (3) of the Exchange Act) other than Vital, or group of persons other than existing stockholders of Vital, becomes the beneficial owner (as defined in Rules 13d-3 and 13d-5 of the Exchange Act) of fifty percent (50%) of total voting power of the voting stock of Vital. Notwithstanding any provision herein to the contrary, the restrictions set forth herein shall not apply to any sales of Vital Common Stock by any Lock-Up Participant solely for the purpose of settling Tax expenses in connection with the consummation of the Transaction.

No provision in this Lock-Up Agreement shall be deemed to restrict or prohibit the exercise, exchange or conversion by the Lock-Up Participant of any securities exercisable or exchangeable for or convertible into Vital Common Stock, as applicable; provided that the Lock-Up Participant does not transfer the Vital Common Stock acquired on such exercise, exchange or conversion during the Lock-Up Period, unless otherwise permitted pursuant to the terms of this Lock-Up Agreement. In addition, no provision herein shall be deemed to restrict or prohibit the entry into a 10b5-1 trading plan at any time (other than the entry into such a plan in such a manner as to cause the sale of any securities subject to this Lock-Up Agreement during the Lock-Up Period).

The Lock-Up Participant understands that this Lock-Up Agreement is irrevocable and shall be binding upon the Lock-Up Participant’s heirs, legal representatives, successors and assigns.

The Lock-Up Participant understands that if the Exchange Agreement (other than the provisions thereof which survive termination) shall terminate or be terminated prior to Closing, then this Lock-Up Agreement shall be void and of no further force or effect.

(Signature Page Follows)

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(Signature Page to Vital Lock-Up Agreement)

Form of Lock-Up Agreement - Vital Therapies Directors

Lock-Up Agreement

April    , 2019

Vital Therapies, Inc.

15222-B Avenue of Science

San Diego, California 92128

Ladies and Gentlemen:

The undersigned (the “Lock-Up Participant”) is entering into this agreement in connection with that certain Exchange Agreement dated as of January 6, 2019 (the “Exchange Agreement”) among Vital Therapies, Inc., a Delaware corporation (“Vital”), Immunic AG (“Immunic”) and the shareholders of Immunic whereby the shareholders of Immunic will contribute, transfer, assign and deliver all of the Common Shares and Preferred Shares of Immunic (collectively, the “Immunic Shares”) owned by them, and all of their rights with respect to such Immunic Shares, to Vital in exchange for shares of the common stock, par value $0.0001 per share, of Vital (the “Vital Common Stock”), with the result of Immunic becoming a wholly-owned subsidiary of Vital (the “Transaction”) and the Lock-Up Participant, as a holder of Immunic Shares, will receive shares of Vital Common Stock in exchange for his, her or its Immunic Shares in connection with the Transaction. Capitalized terms used but not otherwise defined herein shall have the respective meanings ascribed to such terms in the Exchange Agreement.

The Lock-Up Participant hereby agrees that, without the prior written consent of Immunic (or, from and after the Effective Time, Vital), the Lock-Up Participant will not, during the period commencing on the date hereof and ending 180 days after the date of the Closing (the “Lock-Up Period”), (1) lend, offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, or otherwise transfer or dispose of, directly or indirectly, any shares of Vital Common Stock or any securities convertible into or exercisable or exchangeable for Vital Common Stock (including, without limitation, Vital Common Stock or such other securities which may be deemed to be beneficially owned by the Lock-Up Participant in accordance with the rules and regulations of the SEC and securities which may be issued upon exercise of a stock option or warrant), or publicly disclose the intention to make any offer, sale, pledge or disposition; (2) enter into any swap or other agreement that transfers, in whole or in part, any of the economic consequences of ownership of Vital Common Stock or such other securities, whether any such transaction described in clause (1) or (2) above is to be settled by delivery of Vital Common Stock or such other securities, in cash or otherwise or (3) make any demand for or exercise any right with respect to the registration of any shares of Vital Common Stock or any security convertible into or exercisable or exchangeable for Vital Common Stock, in each case for purposes of clause (1) or (2) above other than (A) transfers of shares of Vital Common Stock or such other securities as a bona fide gift or gifts, (B) distributions of shares of Vital Common Stock or such other securities to current or former, direct or indirect, members, stockholders, limited partners, subsidiaries or affiliates (as defined in Rule 405 promulgated under the Securities Act) of the Lock-Up Participant or to any investment fund or other entity that controls or manages the Lock-Up Participant (including, for the avoidance of doubt, a fund managed by the same manager or managing member or general partner or management company or by an entity controlling, controlled by, or under common control with such manager or managing member or general partner or management company as the Lock-Up Participant or who shares a common investment advisor with the Lock-Up Participant) in a transaction not involving a disposition for value, (C) sales or other dispositions or arrangements involving shares of Vital Common Stock acquired in the open market after the Closing, (D) a bona fide third party tender offer, merger, consolidation or other similar transaction made to all holders of Vital Common Stock involving a change of control of Vital following the Closing (including, without limitation, entering into any lock-up, voting or similar agreement pursuant to which the Lock-Up Participant may agree to transfer, sell, tender or

otherwise dispose of Vital Common Stock or such other securities in connection with any such transaction, or vote any Vital Common Stock in favor of any such transaction), or (E) transfers of shares of Vital Common Stock owned by the Lock-Up Participant in a private transaction; provided that in the event that the tender offer, merger, consolidation or other such transaction is not completed, the Vital Common Stock owned by the Lock-Up Participant shall remain subject to the restrictions contained in this Lock-Up Agreement, provided, that in the case of any transfer or distribution pursuant to clause (A) or (B), each donee, distributee or transferee shall execute and deliver to Vital a lock-up letter in the form of this Lock-Up Agreement; and provided, further, that in the case of any transfer, distribution, sale or other arrangement pursuant to clause (A), (B), (C) or (E) no filing by any party (donor, donee, transferor or transferee) or the Lock-Up Participant, or any director of Vital affiliated with any party (donor, donee, transferor or transferee) or the Lock-Up Participant, under the Exchange Act, or other public announcement shall be required or shall be made voluntarily in connection with such transfer, distribution, sale or other arrangement, other than a filing on a Form 5 made after the expiration of the Lock-Up Period or any required beneficial ownership filings under Section 13 of the Exchange Act. For purposes of this Lock-Up Agreement, “change of control” shall mean the consummation of any bona fide third party tender offer, merger, consolidation or other similar transaction the result of which is that any “person” (as defined in Section 13 (d) (3) of the Exchange Act) other than Vital, or group of persons other than existing stockholders of Vital, becomes the beneficial owner (as defined in Rules 13d-3 and 13d-5 of the Exchange Act) of fifty percent (50%) of total voting power of the voting stock of Vital. Notwithstanding any provision herein to the contrary, the restrictions set forth herein shall not apply to any sales of Vital Common Stock by any Lock-Up Participant solely for the purpose of settling Tax expenses in connection with the consummation of the Transaction.

No provision in this Lock-Up Agreement shall be deemed to restrict or prohibit the exercise, exchange or conversion by the Lock-Up Participant of any securities exercisable or exchangeable for or convertible into Vital Common Stock, as applicable; provided that the Lock-Up Participant does not transfer the Vital Common Stock acquired on such exercise, exchange or conversion during the Lock-Up Period, unless otherwise permitted pursuant to the terms of this Lock-Up Agreement. In addition, no provision herein shall be deemed to restrict or prohibit the entry into a 10b5-1 trading plan at any time (other than the entry into such a plan in such a manner as to cause the sale of any securities subject to this Lock-Up Agreement during the Lock-Up Period).

The Lock-Up Participant understands that this Lock-Up Agreement is irrevocable and shall be binding upon the Lock-Up Participant’s heirs, legal representatives, successors and assigns.

The Lock-Up Participant understands that if the Exchange Agreement (other than the provisions thereof which survive termination) shall terminate or be terminated prior to Closing, then this Lock-Up Agreement shall be void and of no further force or effect.

(Signature Page Follows)

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