Green’s Dictionary of Slang

(US) a penis.

1770		D. Gunston (ed.) Jemmy Twitcher’s Jests 85: So void of wit and common sense, / As not to know the difference, / Betwixt a partridge and a dilly.
c.1850		Peeping Tom (London) 26 101: [cartoon aption] Lady. Well, Count, if you must know, we are going to Piccadilly. Count. Pick-a-Dilly! Well [...] I hope you’ll pick a good one.
1941		in G. Legman Limerick (1953) 37: The end of his dillie / Was shaped like a lily.