Rebbi Tzadok: Why mention this point (lying on his stomach) at all? It is totally superfluous!

Obviously, Reish Lakish allows, Halachically, lying this way (as opposed to the accepted Isur mentioned in Nidah 14a, maybe for all, and at least for himself.

Tosfos (Gitin 47a, DH Kereisi) says that it was their way to lie on their stomach. According to Rebbi Tzadok, it should say "it was his way to lie on his stomach." He quotes sources that lying on the stomach simply helps digestion, and since he ate a lot he needed this position. He explains based on other Gemaras that his eating was like that of a Kohen eating Korbanos, pure holiness with no connection to physical pleasure! Giving food to his body was like bringing a Korban on the Mizbe'ach. (Reish Lakish, in Gitin 47a, says that his stomach was his pillow, meaning that his stomach was as if it was detached from himself, without personal enjoyment.)

In Kodshim, the Din is that she'Lo Lishmah is Kasher and therefore Reish Lakish in his eating, even if a she'Lo Lishmah thought would have occurred, the Korban still would be accepted.

Now it is understood the connection of his lying on his stomach because of his special eating habits, and his specific question in Zevachim: if she'Lo Lishmah is Kesherah, let it also be l'Ratzon, etc.

All the best,

Reuven Weiner