LINN ENERGY, LLC LONG-TERM INCENTIVE PLAN FORM OF EXECUTIVE OPTION AGREEMENT FOR SPECIAL INCENTIVE GRANT (ELLIS)

Exhibit 10.3

LINN ENERGY, LLC

LONG-TERM INCENTIVE PLAN

FORM OF EXECUTIVE OPTION AGREEMENT

FOR SPECIAL INCENTIVE GRANT (ELLIS)

This option agreement (“Option Agreement”) is made and entered into effective as of October 11, 2012, (the “Grant Date”) by and between LINN ENERGY, LLC, a Delaware limited liability company (together with its subsidiaries, the “Company”), and Mark E. Ellis (“Participant”).

WHEREAS, the Company considers it to be in its best interest that Participant be given a proprietary interest in the Company and an added incentive to advance the interests of the Company; and

WHEREAS, the Company desires to accomplish such objectives by affording Participant an option to purchase Units pursuant to the Amended and Restated Linn Energy, LLC Long-Term Incentive Plan, as amended, which is incorporated by reference herein (the “Plan”). Unless otherwise defined herein, capitalized terms shall have the meaning given such terns in the Plan.

NOW, THEREFORE, in consideration of the mutual agreements hereinafter set forth, the parties hereby agree as follows:

1. Grant of Option. The Company hereby grants to Participant an option (the “Option”) to purchase all or any part of an aggregate of [            ] Units, under and subject to the terms and conditions of this Option Agreement and the Plan.

2. Purchase Price. The purchase price for each Unit to be purchased hereunder shall be $40.01 (the “Exercise Price”).

3. Vesting and Option Period. Participant may exercise the Option in whole or in part. Except as otherwise provided herein, the Option shall become vested and exercisable in full on January 19, 2016. Prior to such time, no portion of the Option shall be exercisable unless its exercisability is accelerated as provided in this Option Agreement or the Plan. Except as provided otherwise in this Option Agreement or the Plan, the Option, to the extent not theretofore exercised, shall terminate on the expiration of seven (7) years from the date of grant of the Option; provided, however, that upon the termination Participant’s service relationship with the Company for any reason other than (a) the death or disability of the Participant or (b) termination of the Participant’s service relationship with the Company as a result of a Change of Control, Participant may, until the earlier of (i) 90 days from the date of such termination or (ii) the expiration of the Option in accordance with this Section 3, exercise the Option, to the extent such Option had vested immediately prior to such termination and, thereafter, the Option shall, to the extent not previously exercised, automatically terminate and become null and void.

4. Method of Exercise and Payment. To the extent that the Option has become exercisable, the Option may be exercised from time to time by written notice to General Counsel,

or such other form as may be approved from time to time by the Committee, accompanied by the aggregate Exercise Price for the Units to be purchased and any required tax withholding amount as may be determined in the discretion of General Counsel. The Exercise Price and any withholding shall be payable in cash, by certified check, by bank check or other means provided for in the Plan and approved by the Committee, including without limitation by cashless-broker exercise or the withholding of Units upon the exercise of the Option.

5. General Restrictions. Subject to the terms of this Option Agreement and the Plan, the Option may be exercised at any time, and from time to time, in whole or in part, until the termination thereof as set forth herein, or until all Units covered by the Option shall have been purchased, whichever first occurs. The Option shall not be assignable or transferable except as expressly provided by the Committee.

6. Termination by Company other than for Cause. Upon the termination by the Company of Participant’s service relationship with the Company other than for Cause (as defined herein and as determined by the Committee in its sole discretion), the Option granted hereby shall automatically and immediately vest in full. “Cause” shall mean (a) Participant’s conviction of, or plea of nolo contendere to, any felony, any crime or offense causing substantial harm to the Company (whether or not for personal gain) or involving acts of theft, fraud, embezzlement, moral turpitude or similar conduct; (b) Participant’s repeated intoxication by alcohol or drugs during the performance of his or her duties; (c) malfeasance in the conduct of Participant’s duties, including, but not limited to, (i) willful and intentional misuse or diversion of any Company funds, (ii) embezzlement or (iii) fraudulent or willful and material misrepresentations or concealments on any written reports submitted to the Company; (d) Participant’s material failure to perform the duties of Participant’s employment or service relationship consistent with Participant’s position or material failure to follow or comply with the reasonable and lawful written directives of the Board of the Company; or (e) a material breach by Participant of the written policies of the Company concerning employee discrimination or harassment.

7. Termination by Participant with Good Reason. Upon the termination by Participant of Participant’s service relationship with the Company with Good Reason (as defined herein), the Option granted hereby shall automatically and immediately vest in full. “Good Reason” shall mean any of the following to which Participant does not consent in writing: (a) a reduction in Participant’s base salary; (b) a relocation of Participant’s primary place of employment to a location more than 50 miles from Houston, Texas; or (c) any material reduction in Participant’s title, authority or responsibilities of the Company.

8. Death or Disability. In the case of termination of Participant’s service relationship with the Company due to death or Disability (as defined herein), the Option granted hereby shall automatically and immediately vest in full. “Disability” shall mean the determination by a physician selected by the Company that Participant has been unable to perform substantially Participant’s usual and customary duties for a period of at least one hundred twenty (120) consecutive days or a non-consecutive period of one hundred eighty (180) days during any twelve-month period as a result of incapacity due to mental or physical illness or disease. In the case of termination of Participant’s service relationship with the Company due to death or Disability, Participant or Participant’s estate (or any person who acquired the right to

exercise such Option by bequest or inheritance or otherwise by reason of Participant’s death or by reason of Participant’s Disability) may, until the earlier of (a) one year after the date of death or Disability or (b) the expiration of the Option in accordance with Section 3, exercise the Option and, thereafter, the Option shall, to the extent not previously exercised, automatically terminate and become null and void.

9. Change of Control. Notwithstanding anything in the Plan to the contrary, in the event of a Change of Control (as defined in the Plan), the Option granted hereby shall automatically and immediately vest in full. In the event of the termination of Participant’s service relationship with the Company as a result of a Change of Control, the Participant may, until the earlier of (a) one year after the date of such termination or (b) the expiration of the Option in accordance with Section 3, exercise the Option and, thereafter, the Option shall, to the extent not previously exercised, automatically terminate and become null and void.

10. Termination by Company or by Participant without Good Reason. In the case of (a) termination by the Company of Participant’s service relationship with the Company for Cause or (b) termination by Participant of Participant’s service relationship with the Company without Good Reason and other than due to Participant’s death or disability, Participant shall immediately forfeit all rights with respect to any unvested Options. Participant hereby agrees to undertake any action and execute any document, instrument or papers reasonably requested by the Company to effect such forfeiture of the Option resulting from any such termination.

11. Rights as a Unitholder. Participant, or a transferee of the Option, shall have no rights as a holder of a membership interest in the Company except as to any Units actually purchased pursuant to the exercise of the Option.

12. Plan Controlling Document. Participant agrees that the Plan is the controlling instrument and that to the extent there is any conflict between the terms of the Plan and this Option Agreement, the Plan shall control and be the governing document.

13. Limited Liability Company Agreement. As a condition to the exercise of the Option, Participant agrees to be bound by all applicable provisions of the Company’s limited liability company agreement, as it may be amended from time to time.

14. Taxes. The Company and any affiliate thereof are authorized to withhold from any payment relating to the Option, or any payroll or other payment to Participant, amounts of withholding and other taxes due or potentially payable in connection with the exercise of the Option, and to take such other action as the Committee may deem advisable to enable the Company, any affiliate, and Participant to satisfy obligations for the payment of withholding taxes and other tax obligations relating to the Option. This authority shall include authority to withhold or receive Units or other property and to make cash payments in respect thereof in satisfaction of Participant’s tax obligations, either on a mandatory or elective basis in the discretion of the Committee.

15. Issuance of Units. The Company shall not be obligated to issue any Units pursuant to the Option at any time when the Units covered by such Option have not been

registered under the Securities Act of 1933, as amended, and such other state and federal laws, rules or regulations as the Company or the Committee deems applicable and, in the opinion of legal counsel for the Company, there is no exemption from the registration requirements of such laws, rules or regulations available for the issuance and sale of such Units.

16. Notices. Any notices given in connection with this Option Agreement shall, if issued to Participant, be delivered to Participant’s current address on file with the Company, or if issued to the Company, be delivered to the Company’s principal offices.

17. Execution of Receipts and Releases. Any payment of cash or any issuance or transfer of Units or other property to Participant, or to Participant’s legal representatives, heirs, legatees or distributees, in accordance with the provisions hereof, shall, to the extent thereof, be in full satisfaction of all claims of such persons hereunder. The Company may require Participant or Participant’s legal representatives, heirs, legatees or distributees, as a condition precedent to such payment or issuance, to execute a release and receipt therefor in such form as it shall determine.

18. Successors. This Option Agreement shall be binding upon Participant, Participant’s legal representatives, heirs, legatees and distributees, and upon the Company, its successors and assigns.

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IN WITNESS WHEREOF, the parties hereto have executed this Option Agreement to be effective as of the day and year first above written.