Green’s Dictionary of Slang

a thief; thus lime-fingered adj.

c.1499		Skelton Bowge of Courte line 509: Lyghte lyme-fynger, he toke none other wage.
1584		Three Ladies of London II: To catch it, and snatch it, we have the braue skill. Our fingers are lime-twigges, and Barbers we be, To catch sheetes from hedges most pleasant to see.
1596		J. Harington Metamorphosis of Ajax E4: A certaine Gentleman that had his fingers made of lime twigges, stole a peece of plate.
1604		Marston Malcontent V ii: Go thou, the duke’s lime-twig! I’ll make the duke turn thee out of thine office.
1614		Jonson Bartholomew Fair IV iii: How now, lime-twig? Hast thou touched?
1639		J. Clarke Paraemiologia 270: Light finger’d [...] His fingers are lime-twigs.
1641		Harper in Bentley’s Misc. (1837) Feb. 180: Every finger of theirs is a lime-twigge with which they catch dotterels.
1670		J. Ray Proverbs 175: His fingers are lime-twigs. Spoken of a thievish person.