Where does “ლეჩხუმი” come from?

ლეჩხუმი (Georgian) comes from Svan ცხუმ, from Proto-Kartvelian *cxeml-.

Ancestry of “ლეჩხუმი”, step by step

Step	Language	Word	Meaning
1	Svan	ცხუმ	—
2	Proto-Kartvelian	*cxeml-	—