Do you have to pay sales tax twice if you buy out a lease and then immediately sell the car to someone else who lives in a different state?

You will pay sales tax when you buy-out the lease. The seller doesn't pay sales tax and a private party cannot collect it, but the buyer probably will have to pay his state sales tax before he can register the car.

In fact, if the buyer is obligated to pay the sales tax in the state within a certain time where he purchased the car and fails to do so, there can be interest and penalties added to the tax obligation. For instance, in MA you must pay within 20 days of purchase if you're registering in any other state, but you might not register within 20 days, meaning you would have penalties and interest added to your MA tax bill until you paid the 6.25 percent sales tax.