“luke” derived from “lew” or “lewk” or “leuk”, in Middle English, which meant “tepid” (slightly warm). This in turn came from the Old English adverb “hlēowe”, which means “warm or sunny”. Finally, “hlēowe” came from the Proto-Germanic *hlēwaz, meaning “warm”.
The word “lukewarm” popped up around the 14th century as meaning “slightly warm”. Within two centuries, it also began having a figurative meaning, that of “lacking in enthusiasm”.