Green’s Dictionary of Slang

(Aus.) a schooner, which in Aus. is a tall beer glass; thus beer or a glass of beer.

1983		J. Byrell (con. 1959) Up the Cross 8: ‘Three lilies of Tooheys, two of Resch’s’.
1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 11: ‘I’ll have a Lily of Laguna and a Tom Thumb chaser please,’ he said to the jump as he casually dropped a couple of Oxfords on the near and far.
2002		Pete’s Aussie Sl. Home Page 🌐 Lily of Lagoona: a schooner, a beer.