If they are start turning to brown I'd cut it to close to ground.
Because it has seeded and ready to die down.
If you want them to rebloom you could have deadhead as soon as flower peaks are ended and don't let it go seedling. then maybe you could have another flowers coming . try it next year hehe.
For lillies I don't know your kind but for my lillies which are from bulbs. When flowers gone and only leaves left, I keep watering and feeding and don't cut them til they go brown and naturally dies down.
Becuase that's how they accumulate nutritions to come back next year
Even leaves don't die back I;d be just keep feeding(til early fall) and watering. maybe you may have 2nd bloom(still early summar)
Fall or late winter is good time to transplant
if they are in pots shake off loose dirt and loosen a root abit, replant in slightly larger pots with fresh potting mix. if on ground dig around the plants carefully not to disturb roots much. then replant in new location with good amended soils.
Either way water plants very well for a week or so.
