I don't think Lisp is a functional language like Haskell is. It's more of a language with no paradigm. You can do objects, you can do pure functions, you can write your own language easily. And the mainstream languages, like Java, C#, Ruby, Python have also been mixing up different paradigms. You have some kind of lambdas, maybe even closures. They rely heavily on objects and having mutability everywhere is still too common.
I don't think it did. Lisp itself didn't become popular, but a lot of functional ideas are being implemented in more mainstream programming languages, and some functional languages are also becoming popular.