Green’s Dictionary of Slang

(UK Und.) playing cards, as used by a confidence trickster or card-cheat; thus fig., any snare.

1592		Greene Blacke Bookes Messenger 3: The Cards to be called, the Limetwigs.
1608		Dekker Belman of London F2: The wine the Strap, and the cardes the Limetwigs.
1640		Fletcher Night-Walker IV i: My Master stayes, I doubt his lime-twigges catch not.
1699		‘A New Ballad upon a Wedding’ in Playford Pills to Purge Melancholy I 84: She glides as if there were no ground, / And slily draws her Nets around, / Her Lime-twigs are her Kisses.