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bcg......FICO scores do influence your lease payment. As you would expect, the higher your score the higher the probability your payment will be lower. Thing is, you can't tell by how much unless you go and crunch the numbers with the dealer. Also, be advised dealers do not use your FICO score, they use an auto-enhanced score which always seems to be several points lower (at least, that's my experience).
I"ve been leasing my vehicles since 1996. If you are thinking of leasing, I'd check out a few CU's.