Green’s Dictionary of Slang

(Aus.) a woman; usu. with a defining adj., e.g. good line, nice line, slashing line.

1930		implied in nice-lined
1944		L. Glassop We Were the Rats 5: You seen that new blonde barmaid at the Royal? A real good line. [Ibid.] 35: I’ve got a couple of slashing lines who’ve come from Sydney for the Mayoral Ball. The’re a couple of pushovers.
1953		I. Bevan Sunburnt Country 130: Sorts or Lines, are girls.
1955		N. Pulliam I Travelled a Lonely Land (1957) 233/2: good line (fancy line) – a girl friend.
1960		‘Nino Culotta’ Cop This Lot 27: That hostie’s a slashin’ line.
1968		D. O’Grady A Bottle of Sandwiches 210: ‘There’s some pretty good targets about.’ ‘Some pretty slashin’ lines, too.’.