When I first started growing lilies, I started with pots only 3.5 inches high. (I had no one to council me.) They did fine, but when I went to transplant, Usually found the bulbs sitting at the bottom of the pots. So since then, I use a minimum of 5 inch deep pots. Exceptions are when I plant seeds that I think have little chance of viability. Then, because I can't spare are that room and extra soil, they go into 4 inch deep pots.
