"Lay" is past tense already, so "he lay down". Or, if you prefer, "He stumbleded back into the corner of the cave, and layed down, as he was tireded, and drifteded off back to sleep, dreaming of tiny sheep on meth." I suppose it has a certain caveman charm.
Most of the eggs you (or your favorite local restaurants) can buy in supermarkets in the U.S. come from one of two major chicken-keeping conglomerates, both with abominable records of every sort. You're better off buying from local organic producers. Getting your favorite restaurants to switch may be harder, but you can start by asking them.