If an uninsured person borrows your car and gets in an accident deemed by the other insurance co to be her fault when your insurance has lapsed who is liable the driver or the car owner?

I am sure that there are examples to the contrary, but the car owner is the one responsible for the insurance. It's your car. It's your responsibility to make sure it is insured......it would also be your responsibility to make sure whom ever you loaned it to were licensed and legal.