Rule of thumb for pretty much every type of bulb or corm is to dig a hole 2 to 3 times as deep as the diameter of the bulb... a 2 inch tulip bulb goes into a 4 to 6 inch hole; a half inch crocus can be planted just under the sod. Use "3 times" in the south, especially for tulips at the edge of their range, and use "2 times" for planting in clay soil.
Lilies often like to be fairly deep (3 times diameter, or 6 to 8 inch deep hole), but I think most kinds of lilies can do that cool trick where they hitch themselves deeper with their roots, so if you planted a 2 inch lily bulb in a 4 inch deep hole it would be fine... and if you ever dug for it, you'd probably find it 6 inches deep or more.
There are lots of possible colors with Asiatic lilies, so you'll get a fun surprise next summer!
