A. "Let us borrow your car." This means: "Permit us to borrow your car.", or, "May we borrow your car?". So the meaning is clear: you're requesting that someone lend you his car. The "us" in this sentence means you and any number of other people. The "your" in this sentence refers to the person who owns the car.
B. "Let's borrow Kim's car." In this sentence you're talking to