Our Gemara at the end of Amud Beis, heading into the next daf, speaks of the requirement that the mezuzah be placed on the right side of the doorway when facing it during entry. Shem MiShmuel (Miketz 5) makes a brilliant distinction. The Chanukah menorah is placed on the left side—or, as he says, on the right side facing the exit. Why? It has to do with the function of the mitzvah. The function of the mezuzah is to protect the inside from any of the noxious forces, physical or spiritual, that may come from the outside world. The right side mystically represents the powerful and Godly influence. The home is to be kept sacred. However, the function of the menorah is to publicize the miracle (Shabbos 23b)—in other words, to broadcast a spiritual power outward into the world. So here the menorah is on the right side from the vantage point of egress.

A Jewish home is both a stronghold that protects its occupants and a source that broadcasts its spiritual energies outward. And so it is, and so it shall be.