lid (n.) Look up lid at
"movable or removable cover for a pot, etc.," mid-13c., from Old English hlid "covering, opening, gate," from Proto-Germanic *khlithan (source also of Old Norse hlið "gate, gap," Swedish lid "gate," Old French hlid, Middle Dutch lit, Dutch lid, Old High German hlit "lid, cover"), from PIE root *klei- "to lean" (see lean (v.)), with here perhaps a sense of "that which bends over."

Meaning "eyelid" is from early 13c. Slang sense of "hat, cap" is attested from 1896. As a measure of marijuana, one ounce, 1967, presumably the amount of dried weed that would fit in some commercial jar lid. Slang phrase put a lid on "clamp down on, silence, end" is from 1906; many figurative senses are from the image of a pot boiling over.