Lease document is one (among many) that serves as a proof to USCIS that you two have been living together, as a couple. If you are paying rent to Mrs. Y, ask her to include both of your names in the lease. Send the signed (by all who are renting the premise and Mrs. Y) lease to USCIS along with I-130. Don't forget to send few letters you and your spouse receive in that address, where you live.
(IMPORTANT: I am NOT a lawyer. This is my personal opinion and should not be used as a legal advice)
- Jangali Maanab