First some comments on the original code:
(defun findOther (elem L)
(cond
;; NIL is always false, so you *never* end up using this
;; case. You probably want something like ((null l) '()),
;; NULL is still pretty common for this, but since you're
;; expecting a list, you could use the slighly more
;; descriptive ENDP.
(NIL (null L))
;; When you find an element, you immediately return its
;; counterpart, and don't collect it and continue on to
;; the rest of the list. It's also easier to read if
;; you use more descriptive names like FIRST and SECOND,
;; as in ((eq elem (first (first l))) (second (first l))).
;; It's worth noting that unless you have a specific reason
;; to use EQ, you might want to use EQL, which is the
;; default comparison in most CL functions.
((eq elem (caar L)) (cdar L))
;; Else, you continue to the rest of the list. In my
;; opinion, REST would be more decriptive than CDR here,
;; but recursing and returning the value *is* what you
;; want to do here.
((findOther elem (cdr L)))))
Taking some of those into consideration, we could do something like this:
(defun others (element list)
(cond
((endp list) '())
((eql element (first (first list)))
(list* (second (first list))
(others element (rest list))))
((others element (rest list)))))
All that said, the functions in the standard library
would make this much easier. E.g. using mapcan:
(defun others (element list)
(mapcan (lambda (sublist)
(when (eql (first sublist) element)
(rest sublist)))
list))
(others 'a '((a b) (b c) (a d)))
;=> (B D)