The Minchas Chinuch (mitzvah 98) writes that for many years he was troubled by the Rambam's opinion (Hil Bi'as Mikdash ch 9) that a zar is permitted to light the menorah. The only way this would seem practically possible is if a kohen removed the menorah from the heichal (which a zar is not permitted to enter), a zar lit the menorah, and a kohein then returned the menorah to its proper place. However, this scenario cannot work. The gemara tells us with respect to lighting our Chanukah menorah that the hadlakah and not the hanacha, the lighting and not the placement of the menorah is the mitzvah, and therefore lighting must be done in a spot which is kosher for the mitzvah to be fulfilled. For example, assuming the menorah needs to be placed in public view by a doorway, one cannot fulfill the mitzvah by lighting in one's basement and then carrying the menorah and placing it in its proper location. If so, writes the Minchas Chinuch, the same should hold true with respect to the menorah of the mikdash --lighting done outside the heichal by a zar and then moving the menorah into the heichal should constitute an invalid act of lighting and not fulfill any mitzvah. How then can the Rambam declare that a zar is permitted to light?
One can perhaps answer this question of the Minchas Chinuch with R' Chaim Brisker's explanation of that same Rambam. R' Chaim suggests that the Rambam does not view the act of lighting the menorah in the mikdash as a mitzvah at all. There is a requirement for the menorah to be lit, a chiyuv in the cheftza of the menorah, but how that result is achieved, the process of lighting, is not in-and-of-itself a mitzvah act. It is for this reason that a zar can light.
The Minchas Chinuch's comparison between the halacha of lighting our Chanukah menorah and the mitzvah of lighting the menorah in the mikdash is a false analogy. With respect to the Chanukah menorah, the act of lighting is itself a mitzvah, and must therefore be done in a proper location. With respect to the menorah in the mikdash, the act of lighting is just a preparatory condition but is not itself a mitzvah.
Returning to the issue we raised in yesterday's post, we can now argue that the fact that according to the Beis Yosef the menorah oil was divided into eight equal parts of insufficient oil does not prove that one gets credit for performing a mitzvah with less than the proper shiur, e.g. eating less than a k'zayis of matzah. Lighting the menorah is not inherently a mitzvah act (compare with the Beis HaLevi mentioned yesterday) and hence a lack of shiur is not an impediment to lighting. The same cannot be said of eating matzah where the act itself is a mitzvah.