Will a lender lend on a primary residence while tenant occupied

[Luis Escobar]

Hello BP, I am looking to buy my first deal.. I'm looking to go 5% down conventional as I'll be using it as my primary residence for a few years. Will a bank lend on it as a primary residence if the current owner has a tenant in place with a month left on the lease after I close?? If not, any suggestions on closing a deal like this? Thanks, Lou