The East Hampton Library will screen “Stuart Sutcliffe: The Lost Beatle” Saturday at 1 p.m. The 60-minute BBC documentary, directed in 2005 by Steve Cole, tells the story of Sutcliffe, who became friends with John Lennon in 1957 when both were students at the Liverpool School of Art, and joined the rock group, then known at the Quarrymen, in 1959.