duke of lancaster has 1 distinct synonym spread across 1 of its 1 sense. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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 fourth son of Edward III who was the effective ruler of England during the close of his father's reign and during the minority of Richard II; his son was Henry Bolingbroke (1340-1399)
Synonyms, antonyms and the broader and narrower relations for duke of lancaster come from Princeton University’s WordNet. Full sources and licences.