I've never seen gap insurance provided by the lienholder. It's an insurance policy for you, the consumer.
For example, let's say you lease the car for 48 months and after 24 months your remaining principle is $15,000. At this point you wreck the car and insurance pays you (actually pays the lienholder, BMW Financial) $8,000, claiming that is what the car is worth. You are then on the hook for the unpaid balance, or $7,000.
Gap insurance is an insurance policy you buy to cover your ass in case the above scenario happens to you. On my $30,000 lease gap insurance was a whopping $400, or $8.30/month for 48 months. Definitely worth it. If you wreck and can't afford to pay the leftover gap (and they usually want a lump sum payment), then the lienholder will just pursue you for the money you owe, plus interest, plus late fees, plus collection fees, etc. It's a contract that you have to honor.
Another bonus of gap insurance is that you can max out your deductible on your regular car insurance policy if you want. If you wreck your car, your deductible will be deducted from the total payout, but who cares if they deduct $1000 when you have gap insurance....the whole gap is covered.
In February I wrecked my Land Rover. Insurance company totaled it. My principle was $12,200 and the blue book was about $7,000. I didn't have gap insurance and I almost took it in the shorts. After a lengthy battle with the insurance company, I was able to prove to them that the fair market price of the truck, including all the off-road modifications, was much higher than blue book. More than twice blue book, in fact. I walked away with the full note paid off + $2000 cash (insurance paid off BMW Financial, by the way - BMW owned Land Rover when I purchased the Rover). I let the insurance company keep the $2000 cash in exchange for the wrecked Rover. I'm fixing it myself for much less than the insurance estimate. Now I have a nice off-road toy owned free & clear and a nice daily driver BMW at a killer interest rate due to my continued patronage of BMW Financial.
But after I almost lost big on the Rover wreck, I told myself I would always carry gap insurance.
P.S. I'm not an insurance agent...just speaking from my experience...please correct me if I'm wrong anywhere.