Thanks for including pictures, they say a picture is worth a thousand words!
Here's how I would handle it if these were mine. Others on here may approach this situation differently, however. My general rule is to not move a lily after the nose has turned green and the leaves have begun to unfold. For those in picture #1, I would simply add another couple inches of soil, leaving some of the green exposed. These would then draw themselves deeper into the ground naturally over the summer. Mulch generously around the stems over summer. If they absolutely must be moved, then move very carefully as a clump, keeping the anchor roots and soil intact. Plant a little deeper but still leave some of the new green exposed. Mulch generously during the summer months in either case.
For those in picture #2, I can tell by looking at the noses, it appears that the mature bulbs are at a satisfactory depth already. Except for possibly one, only the immature stem bulblets are exposed. In this case, those can be carefully spooned away and replanted covered by an inch or two of soil.
It appears you have very good soil in very good condition.
