Luke warm (tepid) derives from GERMAN “Lau warm”
If you find written evidence of it being directly borrowed from German by English speakers, the entry would probably be changed. Right now the available evidence shows English did not get the word from German, and that the two words developed separately, perhaps from some pre-German source.
Many languages have cognate words. The fact that two languages have similar words doesn’t show that one language must have borrowed from the other; it only shows that the words have something in common. What they have in common can be simple, or it can be a very interesting question.
It’s not THAT silly, to say “If Language A borrowed this word from Language B, how and when did that happen?” The word is from a time when English speakers and German speakers didn’t live with each other very much.
“Greek must have borrowed the word ‘phobia’ from English, since both languages have it.”
Most people know that’s a false statement. They can quickly prove it by (a) showing that Greek had such a word long before English did, and (b) showing where English speakers wrote something like “Let us use the Greek word ‘phobia’ to describe this phenomenon”.
“Phobia” is an easy one. The “luke” in “lukewarm” is not so easy, but the same principle applies: you have to show how it was done, not just that it’s possible to do it.
Apparently (I might be wrong, I just remember reading about it), one of the Aboriginal languages in Australia has a word “dog”, which means “dog”. There was no borrowing in either direction; we just both happen to use the same sound to mean the same thing. Even if that story is false or a hoax, it’s still a reminder that etymology can’t be done just by looking at words and applying the most convenient logic. If a word is borrowed, some actual people had to do the actual borrowing, at a certain time in a certain place. Often it’s not possible to discover exactly when or exactly who, but it IS often possible to rule out a possibility because there are two groups of people with the same word but they never met.