I've seen far too many lids that were "repaired" with silicone caulk. Ugly, and it doesn't work, and most people are clueless about how to use caulk anyway. So what I've seen are ice box lids that now have a goopy, silicone seal with lots of peaks and ridges to trap the moisture and breed *more* mildew.
After minutes of hard thinking, I came up with this solution which has worked so far... I measured carefully, then roughed up the surfaces. After building a jig around the outside edge and lining it with waxed paper, I poured in a "bunch" of epoxy. Ta - DA! Sand down and paint, and there's a permanent fix.