From Longman Dictionary of Contemporary Englisheyelideye‧lid /ˈaɪlɪd/ ●●○ noun [countable] 
HBHa piece of skin that covers your eye when it is closed His eyelids began to droop (=close, because he was sleepy). The room spun. Her eyelids fluttered (=moved up and down quickly) and she fainted. → not bat an eyelid at bat2(2)
HBHa piece of skin that covers your eye when it is closed His eyelids began to droop (=close, because he was sleepy). The room spun. Her eyelids fluttered (=moved up and down quickly) and she fainted. → not bat an eyelid at bat2(2)Examples from the Corpus
eyelid• Susan, my long suffering wife, who never batted an eyelid as this project unfolded and gave me lots of encouragement.• Smith devised a technique using eight pieces of latex rather than one overall mask, including convincing eyelids.• At the same time as her nose wrinkled, the corners of her mouth turned down and her eyelids drooped.• He notices the fluttering at the corners of her eyelids.• Her eyelids were closing against the sheer enormity of the prospect.• His eyelids were heavy and wet.• My eyelids felt thick and swollen.• My eyelids were swollen shut, and I was drenched with sweat.eyelids ... droop• Twice I ran perilously close to the edge, my eyes dazzled and eyelids drooping.• Tiredness crept over her, making her eyelids droop.• Her eyelids drooped, fluttered, and then drooped again.• Towards the end of his harangue his head grew heavy, his eyelids drooped, and his speech became thick.• One of the issues in his last re- election campaign was that his eyelids frequently drooped during meetings. 