On discovering I would be late for work, I had to leave without finishing my thought:
The really intuitive among us might have extrapolated, but when I stated that seed sown near the surface produce bulbs that want to be deeper, it was meant to segue into a comment that when you cover the exposed bulbs, Calin, the others, being then planted even deeper will be fine.
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This is not to say that planting the seed deeper from the start is better, however.
Species lily seed is usually surface sown, and perhaps raked or slightly mixed with the surface soil. (You'll still see the seeds visible.) Then covered with a quarter to half inch of light mulching material. (I use #2 chic grit). Since wild lily seed is dispersed by the wind, this is close to what nature intended. As species lily seeds tend to be more finicky, this is my recommendation.
Hybrids are usually more vigorous and less prone to overabundant moisture, and are often planted much deeper. I've never worried too much about it, better too shallow than too deep, is my motto, as long as drying out is not a concern.
I don't think we've really discussed this subject much. I'd be interested to know what others' recommendations/experiences are with planting depth....
Edited to change "Anthony" to "Calin".