Green’s Dictionary of Slang

the extreme, the absolute limit.

1954		J. Blake letter 17 March in Joint (1972) 48: There is a trombone man in the band that is the living end.
1961		C. Bingham Run Tough, Run Hard n.p.: Christ, he thought. This was the goddam living end. The kid in hot water again. Molly wise to Irene. He was sick and tired of the whole stinking rat race.
1970		(con. 1950s) H. Junker ‘The Fifties’ in Eisen Age of Rock 2 (1970) 102: She might come across if he were a big wheel, a B.M.O.C. [...] the living end.
1978		R.D. Pharr Giveadamn Brown (1997) 150: This pad was the living end. The main issue.