Yes, an individual can enter into a lease agreement with a Partnership and also be a member of that Partnership. But be aware that one particular issue may arise and needs to be covered in one of the legal documents relevant to this set up.
The person that is the Lessor will also be a Lessee, since partners generally have personal liability for the debts and obligations of the Partnership. Should the Partnership default on the lease, the Lessor may be required to seek recourse against the partnership, which would include potential claims against himself.
Thus, the Partnership Agreement or the Lease Agreement may need to be drafted to address this specific situation.
Details on Standard Legal software for each of these particular titles may be found here:
General Business Partnership Agreement legal forms software