Green’s Dictionary of Slang

(Aus.) an elastic or rubber band.

1993		Aus. Word Map 🌐 lacky band. a rubber band [...] ‘“Lacker band” was in common use when I was at school (50s & 60s) and later at work’.
2013		T. Peacock More You Bet 46: A ‘lazzo’ or ‘lackey band’ as elastic or rubber bands are popularly named.