Green’s Dictionary of Slang

strong and thin n.

[rhy. sl.]

1. (US) gin.

[US]A.J. Pollock Und. Speaks n.p.: Strong and thin, gin.
[US]Maurer & Baker ‘“Aus.” Rhyming Argot’ in AS XIX:3.

2. (US) a hand [= fin n.1 (1)].

[US]St. Vincent Troubridge ‘Some Notes on Rhyming Argot’ in AS XXI:1 Feb. 47: strong and thin. Fin. (Origin uncertain, probably English.) Agreed, but rare compared to Lincoln’s Inn (one of the English legal Inns of Court in London).