WordNet records no synonym and no antonym for lie awake. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
lie without sleeping
“She was so worried, she lay awake all night long”
Synonyms, antonyms and the broader and narrower relations for lie awake come from Princeton University’s WordNet. Full sources and licences.