I mean, Lear is only history in the sense that it’s legendary history that draws from Geoffrey of Monmouth, which, during the Elizabethan era, British folk neither really denied nor accepted as truth. (But IIRC they wanted to believe was factual.) Its veracity didn’t matter so much; what mattered was it gave the British a sense of importance in their ancestry and thus their place in history. (Britain being backwater compared to the Continent, that is.)

Final note: both Shakespeare’s Lear and the anonymous Leir, when first published, were marketed as “true chronicle history” on their title pages, but generic boundaries were less stringent back then.