We do need to send our leases as supporting documents after all, right?
for the
application, the guide clearly states leases OR Tax returns (we sent tax returns and it was fine, so i'm sure of that; in the IL they did ask to bring other supporting evidence, such as leases, bank accounts, etc, but didn't single out leases, and that letter is a form letter normally, not specific to applicant AFAIK);
but then
IN the interview, they might ask for leases as supporting evidence, depending on how convinced they're otherwise.
I think they always mention other supporting evidence, but if they clearly see that the relationship is genuine, they may not be very strict with them; all depends on what impression IO gets from the original application, I think. But one should always assume that they need them, otherwise they wouldn't mention it in the application and/or IL letter.
in my personal case, when I got GC, the IO hardly looked at any "supporting" evidence (of rel.ship/marriage), although we had them ready; our case is a clean, straightforward one, and we never had any problems...so far, N-400 looks to be the same.
In your case, because you lived separate, you should take ANY and EVERY piece of evidence/documents you can get your hands on, just to be ready. better be safe and over-prepare than vice versa.