And behold, on this the Rambam writes -
The lighting of the Menorah candles is Kosher if done by a none Israelite, therefor if the Priest/Cohen cleaned out the candles, and brought them outside of the sanctuary, it is permissible for a non Israelite to light them.
The main part of the Mitzvah here is for the priest to improve the candles, which is the clean out the Menorah and the wicks.
Our question over here is that isn't the setting up of the Menorah just the preparation for the commandment, so how can we say that the preparation for the commandment must be carried out only by a priest, but the commandment itself can be done by anyone? Including a non Israelite?
And we will explain the matter by stating that we know a candle is compared to a humans soul. As it says below by King Solomon -
(27) The soul of man is the lamp of the LORD Revealing all his inmost parts.
As well is it also comparable to a Mitzvah/commandment, as we see from King Solomon again below -
(23) For the commandment is a lamp, The teaching is a light, And the way to life is the rebuke that disciplines.
And behold, regarding a soul, is is upon the righteous of the generation to clean out the souls of the people from all sin and iniquity, and to purify their hearts to come closer to The Creator, Blessed be He. However, when it comes to fulfilling the commandments, then that is incumbent upon all humanity to themselves fulfill the act of the commandment, and the righteous cannot fulfill it for them.
And with this we can understand the position above of the Rambam, that the commandment to prepare the candles of the Menorah is a hint to the preparation and and fixing of the soul, which is in itself compared to a candle, which can only come through the priest, who is analogous to the righteous.. however, the lighting itself of the candle, is also comparable to the doing of all the commandments, which is also compared to a candle (as we saw with King Solomon), and this happens through the individual acts of everyone, and even a non Israelite has what to do with the commandment of lighting the candles.