G'day
My guess is that D&D's liches are inspired at least in part by a story by Robert E Howard. I don't remember the title of the story, but I do remember one of Howard's stories of Hyboria that was about a necromancer's body spontaneously reanimating. In that story Howard used the archaic English word 'lich' for the reanimated corpse. Now 'lich' means (or then meant) 'corpse, cadaver, dead human body', and Howard meant to emphasise its deadness, not its animation. But when Gygax was looking for a word to specifically denote a *reanimated* necromancer, the Howard story might have come to mind. Having almost completely fallen out of use, 'lich' was suitable to have a specialised meaning thrust upon it.
By the way, although 'lich' might be cognate with German 'Leiche', it is derived from Anglo-Saxon, not from German.
And this is etymology (or philology), not semantics. Etymology ought not to be confused with entomology, which is the study of insects.
Regards,
Agback