Here is what I've found: On at least two TV appearances (I assume in the UK) in 1966, even though the Lads were lip-syncing, Paul sings on the first part of the lines in the verses, John joins in for the rest of the lines. Paul: "Got a good reason" Paul and John: "For taking the easy way out."
Munich concert footage, 1966: Same as above. George joins in for the chorus.
Japan concert footage, both shows, 1966: Paul and John share the entire verses, George joins in for the chorus.
My recollection from DC concert, 1966: John steps up to his mic first, sings. Paul steps up to his mic for second half of first line. Both remain at mics throughout the rest of the song. I'm guessing Paul was merely late stepping up to the mic for the first verse.
All three examples: George plays the opening riff, appears to play at the guitar break.
My opinion: Paul and John sang on the record as they sang on TV and in the Munich gig. Chronologically, these occurred prior to the Japan shows, but after the track was recorded. Though John gets credit for "inventing" the riff, George played it on the record and in concert. Guitar break: inconclusive. John claims it was his, but you can judge the existing videos and form your own opinion.
John on lead guitar: Setting their later work aside, I can't find any footage of the Beatles in concert between 1963-1966 which shows John playing lead guitar on "Long Tall Sally" or "You Can't Do That", even though most Beatle-People know he did on the recordings. (John on LTS on one break only). The closest I've found was from their Australia concert, which focuses only on Paul and George during the break, not John. George does NOT appear to be playing the guitar solo at the break, but repeating the opening riff under what I would assume to be John's guitar solo.
Anybody have links to other live performances of "DT", "LTS", or "YCDT" to show John playing lead guitar in concert, not including John playing second lead on "I Feel Fine"? Just curious.