If I pay extra on my auto lease, does that go towards the buy out price for the end of my lease? For example if im paying 400 a month for 48 months and my residual value is 11,500 at the end of the 4 yrs does anything over the 400 a month payment go towards that 11,500 amount?
You should refer to your contract. But usually it won't. Every over-payment will be counted toward the next payment. So of you pay the first month 450, the second will be billed as 350 and so on.
So on paper, if you pay 450 every month, at the end you will have 2400 of over-payment. Which then leaser can book (usually after your written request) that amount as part of buy out price so you would have to pay 9100.
But doing so will yield you no benefits. You could put that extra 50 in saving account (as per RonJohn comment) and after 48 months have more money to buy back than 2400.
Doing that will not only give you more money in the end but you have more control over the money. Your leaser is not a bank or saving account, so taking out any amount would require from you doing extra paperwork (or any work in general). Having the money in your bank account you give you ability to pull any amount on request, put any amount in on any given day and use to to have highest yield profit in those 48 months.