Green’s Dictionary of Slang

(Aus.) a habitual drunkard.

1919		W.H. Downing Digger Dialects 47: steady lapper — An inveterate drunkard.
1924		(con. WWI) A.G. Pretty Gloss. Sl. [...] in the A.I.F. 1921–1924 (rev. t/s) n.p.: steady lapper. An inveterate drunkard.