Ho to compare two list in lisp ?

This question doesn't quite make sense.
To compare requires some kind of comparison operation.
If you can't use any of the "eq"-type operations, how do you expect to compare the elements of the lists?
For numbers you could subtract and use (zerop ...), but that's an obvious HACK!
Is your question about how to walk the lists "in parallel"? How to structure the overall comparison? Looping vs. recursion vs. some of both?
Use the "Improve question" to clarify what you are really trying to solve.
(Since comparison of lists is already available in lisp, this looks like a homework assignment type of question.)