I also started consistently beating the lich (on loop 6-ish, I think?) after getting two specific kinds of cards through town upgrades:
(tiny, early game card spoilers ahead)
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Villages - give you quests to kill specific monsters along the path and experience points to unlock new abilities during the run
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Wheat fields - must be put next to villages, but spawn scarecrow enemies that seem to consistently drop two good pieces of gear per kill.
I wasn’t aware of lich palaces. I assume because I normally built things around the campfire? So I didn’t know the first boss could be harder.