I visited Hatfield House a while ago, where Queen Elizabeth I lived as a child. On one wall there is a family tree for her, painted as a tree with leaves. Amongst the people it shows are Macbeth, King Lear and Adam and Eve. I know Macbeth was real - although Shakespeare wrote fiction about him. I know Cymbeline was a real Roman client King too. But I've never seen direct evidence about King Lear.
So is he known? And did he have three daughters, whether or not they followed the plot of the play? When did he live?
The earliest reference we have to King Lear/Leir is in Geoffrey of Monmouth's 12th c. Historia Regium Britanniae (history of the Kings of Britain) which is also the work that introduced English readers to the Welsh legends of King Arthur. Monmouth places his reign in the 8th c, but other later sources place it far further back in the past.
Although we don't have any earlier Celtic or English sources for King Lear, it's reasonable to assume that the same debate about historicity that applies to King Arthur applies to Lear, since it's likely that Monmouth used sources which we don't have, rather than making up the story from scratch.
If we accept the goodwill of Monmouth, that he recorded a received 'history' we then have the question of whether Lear was a real historical figure whose existence was passed down through the generations by means such as oral story telling or whether he was a figure in Celtic mythology who was transformed over time in to a legendary King.
Long story short: We just don't really know.
http://www.rsc.org.uk/explore/shakespeare/plays/king-lear/sources.aspx