Do put soil around the pots if you put them in the bed(s). The lilies will appreciate the temperature mediation that it provides, and you won't need to water as often. Burying the pot up to the lip is best, but even with the soil only half way up the pot, it is a significant plus. Remember, when you water, you care about the moisture inside
the pots, not outside. There will likely be a big difference.
I guess everyone knows what a cloth bed is, except me....
Is it a temporary pseudo greenhouse (covered with cloth)?