WordNet records no synonym and no antonym for lunar day. 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.
the period of time taken for the moon to make one full rotation on its axis (about 27.3 sidereal days)
Synonyms, antonyms and the broader and narrower relations for lunar day come from Princeton University’s WordNet. Full sources and licences.