Your error

You are passing to evenp n instead of (car L).

Iteration

This is relatively easy to implement using loop:

(defun even-greater (n l)
  (loop for k in l
    when (and (< n k)
              (evenp k))
    return k))

(even-greater 5 '(1 2 3 4 5 6 7 8))
==> 6

Recursion

If you are required to use recursion, you can do it too:

(defun even-greater (n l)
  (cond ((endp l) nil)
        ((and (< n (first l))
              (evenp (first l)))
         (first l))
        (t (even-greater n (rest l)))))

(even-greater 3 '(1 2 3 4 5 6 7 8))
==> 4

Library

And, of course, Lisp has a very powerful library, including find-if:

(defun even-greater (n l)
  (find-if (lambda (k)
             (and (< n k)
                  (evenp k)))
           l))

(even-greater 2 '(1 2 3 4 5 6 7 8))
==> 4