If they are asiatic lilies, the bulbs will something like these:
Roots growing from the stem above the bulb(s) can be discarded. They will die in the fall if they haven't already.
The roots originating from the bottom of the bulb(s) are fairly permanent. You will want to keeps as much of these intact as possible. But don't be too concerned because it's not critical. Even if all the roots were removed, the lily would still easily survive.
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