Same as the core iterate function except the lazy sequence ends when the value is nil.

iterate-while.clj

(defn iterate-while-1
  [f x] 
  (when x
    (cons x (lazy-seq (iterate-while f (f x))))))

(defn iterate-while
  [f x] 
  (take-while identity (iterate f x)))
    

Upon further reflection, it is not needed. Simply apply take-while to iterate.