I have an Audi A4 with about six weeks left on the lease. Can I let another family member drive that car? They don’t live at same address, but have their own comprehensive car coverage (albeit, on a Prius). I am using Audi Financial.
If something happens to the car, which insurance policy covers it? And who would have to pay?
that would best be answered by your insurance company rather than a bunch of random forum members who may or may not be experts 
Should be covered by whoever is driving, but leasing companies require minimum coverage. So, there may be a problem, if they don’t have enough coverage. But 305 is right, talk to your insurance (and maybe Audi).
I think insurance follows the car, not person. In this case, OP needs to keep insurance and if his family member gets in an accident in the A4, OP’s insurance would cover it and would also be affected (ie his rates would go up).
Liability will be covered by the driver. Comp and collision would be the owner’s policy.
@jon beat me by a hair 
that’s effectively 1 payment left, not worth the risk over 1 payment. If you take out another Audi I think there’s pull ahead program anyway so you can just get rid of car now (at least they have 3-mo pull ahead programs all the time, not sure if they currently do)
@Carterman32 - ignore me, thanks guys. I get into vhooloo’s territory with 50% rate 
I would call insurer. Contrary to what some of said here, my father got in an accident in my car and his insurance covered everything. Like in a rental car, your insurance follows you. The main limitation would be if the other persons insurance wasn’t good enough, had higher deductible or they don’t carry collision and comprehensive.
Different state insurance regulations may also be relevant.
That was my understanding also.
It 100% depends on the auto insurance policies involved. More than likely it will all follow the car. However, some policies are written in a way that the liability coverage may follow the driver of the car if driver is covered by their own policy. Best bet is to discuss with your agent.
Respecting all the great answers above and coming from personal experience. Do NOT let anyone that is not on your insurance policy drive your car, unless you can claim they stole it 