lake (n.1) Look up lake at
"body of water surrounded by land and filling a depression or basin," early 12c., from Old French lack (12c., Modern French lac) and directly from Latin lacus "pond, pool, lake," also "basin, tank, reservoir" (related to lacuna "hole, pit"), from PIE *laku- "body of water, lake, sea" (source also of Greek lakkos "pit, tank, pond," Old Church Slavonic loky "pool, puddle, cistern," Old Irish loch "lake, pond"). The common notion is "basin."

There was a Germanic form of the PIE root which yielded Old Norse lögr "sea flood, water," Old English lacu "stream, pool, pond," lagu "sea flood, water, extent of the sea," leccan "to moisten" (see leak (v.)). In Middle English, lake, as a descendant of the Old English word, also could mean "stream; river gully; ditch; marsh; grave; pit of hell," and this might have influenced the form of the borrowed word.
lake (n.2) Look up lake at
"deep red coloring matter," 1610s, from French laque (15c., see lac), from which it was obtained.
lake (v.) Look up lake at
"to play, sport," Old English lacan (see lark (n.2)).