in addition to what others said, maybe check him while he's sleeping, maybe he just breathes through his mouth and it makes his lips dry.
My little one seems to be quite a warm baby, and on warmer days he has just been a little more demanding on the food front, but he is bb fed so he just gets extra on those days.
if it's just his lips there is some stuff alled marcalan that is intended for nipples, but also makes great lipgloss and won't hurt bubs.

But I think with the water at the end of the day being dehydrated is worse for the kidneys than a few mils of water would be, maybe judge it on the contents of his nappy iykwim (no wee or hard poo could mean he needs more liquids)