Where does “lith” come from?

lith (Old Danish) comes from Old Norse hlið, from Proto-Germanic hlidą, from Proto-Indo-European ḱlitós, from Proto-Indo-European ḱley-, from Proto-Indo-European ḱel- — to cover; to incline.

Ancestry of “lith”, step by step

Step	Language	Word	Meaning
1	Old Norse	hlið	gate; side; a gap, gate, space
2	Proto-Germanic	hlidą	lid, cover
3	Proto-Indo-European	ḱlitós	covered, sheltered; leaning, sloped, inclined
4	Proto-Indo-European	ḱley-	to shelter, cover; to lean, slope, incline
5	Proto-Indo-European	ḱel-	to cover; to incline

Every word from Proto-Indo-European ḱel- →

lith — Etymology, Origin & Word History | Etymology Explorer