Likutei Sichos vol. 06 page 26 ff. [Same as class sixty three Sicha, but discussing the beginning and the end rather than the middle]. Moshe the redeemer needed to be above the limitations of all (3) levels of exile, his mother, therefore, was conceived outside of Egypt, and miraculously became young to give birth to Moshe. This is connected (not only with leaving Egypt, but also) with the entry into Eretz Yisroel.
