From 2 Broke Girls:
I'm going to the prom with Brandon, if his dad will lend him the car.
Why does the quote use "if ... will"?
After reading this ELL question, I think it should be if ... would
"Will" does not always function as a future marker; it can be used to mean "be willing to." So your sentence amounts to "I'm going to the prom with Brandon, if his dad is willing to lend him the car."