We locked our rate for a refi, but my lender says if rates come down we can float it down.

You may be referring to what some call a "free float down". Generally when these are offered, the initial rate is higher to begin with as nothing is truly "free".

A lock and float are two different things. When you are locked, your rate is what they locked it at. Its also a commitment for funding, or to reserve funding money to purchase the loan. A floating rate, is when you are not locked, and you are not commited to any rate.