Green’s Dictionary of Slang

line n.3

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

implied in nice-lined
[Aus]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.
[Aus]I. Bevan Sunburnt Country 130: Sorts or Lines, are girls.
[Aus]N. Pulliam I Travelled a Lonely Land (1957) 233/2: good line (fancy line) – a girl friend.
[Aus]‘Nino Culotta’ Cop This Lot 27: That hostie’s a slashin’ line.
[Aus]D. O’Grady A Bottle of Sandwiches 210: ‘There’s some pretty good targets about.’ ‘Some pretty slashin’ lines, too.’.

In phrases

nice-lined (adj.)

of a woman, having an attractive figure.

[US]R. Whitfield Green Ice (1988) 31: Big, nice-lined moll.