A Lisp programmer working in C might feel the constraints of the language. But their style would still show the Lisp influence, and they would be more likely to, for instance, take a heavily recursive solution or reach for pointers to functions than a person raised on C would. They just conceive of things differently.

However it is easier to program like you are in another language when all of that other language's features are supported in the one that you have.

Cheers,
Ben