from Eric Raymonds essay, How to become a hacker:
LISP is worth learning for a different reason — the profound enlightenment experience you will have when you finally get it. That experience will make you a better programmer for the rest of your days, even if you never actually use LISP itself a lot.
However, I want concrete examples (methodologies)
Lisp makes you think in terms of higher level memory structures than just other than bytes and pointers to structs.
The 'lists' and all the operations that you can perform on them will initially feel terribly inefficient (filter??!), but this will literally free you from having to think about how stuff is laid out in memory.
The upshot of that is that you will see more clearly what the real solution is to your problem.
As for functional programming, that in and of itself is a great way to get an alternative look at your programming.
For a fantastic example of that look at the 'hashlife' code, it's written in C but it could only have been done by someone with a profound insight in to the benefits of functional programming.
The reverse is also true, learning C as a lisp programmer will make you a better lisp programmer.
In fact I doubt that there is any language that does not have to contribute some unique bit to the world of programming, and that will enrich you if you learn it to some level of proficiency.