What is "Lechem Kodesh"?
Radak citing Menachos 95: It was Lechem ha'Panim.
Malbim: It is Terumas Lachmei Todah 3 (from each of the four kinds of Lachmei Todah, one loaf is given to the Kohen who offered it; only Kohanim may eat it). This applies only when there is a Bamah Gedolah 4 (of the Tzibur; Zevachim 117b); even so, the custom was to separate it, just like they used to separate Chazah v'Shok, even though they do not apply on a Bamah.
Lachmei Todah is eaten only on the day it is offered and the next night; one may not offer Todah on Shabbos. We can resolve this with the opinion that he came on Shabbos, i.e. Friday night, but then we cannot explain "Lechem ha'Panim ha'Musarim" (verse 7) to be what was removed from the Shulchan. (PF)
All Kodesh bread other than Lachmei Todah is forbidden to Zarim. (PF)
Perhaps the owner of the Todah took the remaining 36 loaves to another city. When the Mishkan was in Nov, Kodshim Kalim could be eaten in all cities of Yisrael (Zevachim 14:7). (PF)
It is clear from Yerushalmi Megilah 1:12 that there was a Bamah Gedolah in Nov, and so say Rashi (Megilah 9b) and all the Meforshim! This requires investigation. (PF)
Why did he say "Im Nishmeru Ach me'Ishah"?
Rashi: I am reluctant to feed them to Zarim - and even this is possible only if they are Tehorim.
Radak: He meant, Im Nishmarta (if you are Tahor). He did not explicitly say so, due to honor. This is like "v'Yardu Chol Avadecha Eleh Elai" (Shemos 11:8; for Pharaoh's honor, Moshe did not say you will come to me).
Malbim citing Parshas Derachim: We transgress the smallest Isur necessary to save a life. It is better to feed Kodesh [to Zarim] than Terumah, if they are Tehorim - Misah bi'Ydei Shamayim is only for Terumah. If they are Temei'im, it is better to feed them Terumah, for there is Kares for a Tamei who eats Kodesh.
QUESTIONS ON RASHI
Rashi writes that he was reluctant to feed the Lechem Kodesh to Zarim [but not that it was forbidden]. Why was he reluctant?
According to Malbim (refer to 21:5:1:2 and the note there), the custom was to separate Terumas Lachmei Todah. L'Chatchilah they treated it like Terumas Lachmei Todah, and only Kohanim would eat it.
Assuming that it was Lachmei Todah, it belongs to the one who offered it, except for the loaves made Terumah (refer to 21:5:1:1**, 21:5:1:2). After the owner took what he and his invitees expected to eat (one may not leave any over until dawn), Achimelech preferred that Kohanim eat the rest, for (a) they are zealous [about Taharah and the other laws of eating Kodshim], or (b) the Kohanim received bread rarely, for Todos were not offered so often. Even if the owner took little, each of the 85 Kohanim in Nov received about 10 k'Beitzim for him and his family, or even less, if there were more than 85 (refer to 22:18:2:1). (PF)
