induction l as [ | x xs IHxs].
+ intros; exists ([], l'); auto.
+ intros l' LE; destruct l' as [ | b bs] eqn:LEq.
- inversion LE.
- pose proof IHxs bs as IH; clear IHxs.
assert (LE' : le (length xs) (length bs))
by (simpl in *; omega). (* Overkill? :) *)
clear LE.
apply IH in LE'; clear IH.
inversion LE' as [pair Split]; clear LE'.
destruct pair as [l1 l2] eqn:Pair.
simpl.
rewrite Split.
exists (b :: l1, l2).
simpl.
auto.
Qed.

(* Specifications: *)
Lemma lengthSplit2 : forall {A : Type} (l l' l1 l2 : list A),
lengthSplit l l' = Some (l1, l2) -> l1 ++ l2 = l'.