I think this is the opposite for lions? I'm only going by the fact that the Buddha is shown sleeping on his right side all of the time and that this is called the lion pose (not the same as the yoga lion pose). He slept on his right side in the same way male lions sleep on their right side.

(I first learned this because I was researching why when I meditated on my right side I would sometimes have hallucinogenic visions, but not on my left side - it was a surprise to come across this fact about the Buddha)