Wodehouse also used the phrase...
This page speaks of the song "Could Lloyd George Do It?" being performed in a revue in Australia in 1925; and this page says it's on a Columbia 80rpm record by Stanley Lupino. Released September 1925.
Most notable seems to be an article entitled 'Can Lloyd George Do It?', which was published in May 1929 (John Maynard Keynes and H.D.Henderson, 1929; JMK.9, pp.86-125).

So, is this a song about economics?
-Joe-