(defun count-eq (lst &optional (c 0) (p (car lst)))

  (cond ((null lst) c)

        ((eq p (car lst)) (count-eq (cdr lst) (+ 1 c) p))

        (t c)))

==> count-eq

;; Проверка

(count-eq '(a a a b c d))

==> 3

(count-eq '(a a b c d))

==> 2

(count-eq '(a b c d))

==> 1

(count-eq '(a a a))

==> 3

;; решение задачи

(defun task (lst)

  (apply 'max (maplist #'count-eq lst)))

==> task

(task '(aa aa ab ac ac ac ad ae af af af af aa aw))

==> 4