Biolife "lease agreement"

Hey guys, I've been renting a room for two months with a nice older lady, and I see that at the Biolife donating centers they require a "lease agreement" to be printed out.

I have done this, but on my ID It shows my previous address. Will they accept my "printed out Lease Agreement" with both mine and my landlords signatures, and other details, with my current id stating that I live in another city?