Green’s Dictionary of Slang

drain v.

also drain off

to urinate; usu. in combs. below.

[US]Monteleone Criminal Sl. (rev. edn) 75: drain To urinate.

In compounds

drain-off (n.)

an act of urination.

[UK]J.J. Connolly Layer Cake 59: Need a good drain-off before I get in the motor.

In phrases

drain one’s/the (main) vein (v.)

(orig. Aus.) to urinate.

[US]Baker et al. CUSS 218: Vein, drain the Urinate.
[US] P. Munro Sl. U.
OnLine Dict. of Playground Sl. 🌐 Drain the main vein v. to urinate in a particularly speedy manner (probably to avoid being caught doing it in a public place), e.g. in a shop doorway or telephone box on the way home from the pub.
[US]F. Bill Donnybrook [ebook] ‘Smells like some sour son of a bitch drained his vein back here’.
drain the dragon (v.) (also drain the lizard, …snake) [dragon n.4 /snake n.3 ]

to urinate.

[Aus]B. Humphries Barry McKenzie [comic strip] in Complete Barry McKenzie (1988) 30: Just hang while I nick out the gents and drain the dragon.
[US] P. Munro Sl. U.
[Aus]Age (Melbourne) 7 Dec. 130/5: Australia has much of which to be proud [...] drain the dragon, syphon the python, (point percy at the porcelain), having a liquid laugh down the great white telephone.
[Ire]P. Howard Miseducation of Ross O’Carroll-Kelly (2004) 75: I tell her I have to drain the snake. [Ibid.] 195: I tell the girls I need to drain the lizard.
[US]S. King Finders Keepers (2016) 29: Pull in there [...] I need to drain the dragon.
drain the lily (v.)

see under lily n.

drain the snake (v.)

(Aus.) to masturbate.

[Aus]S .J. Baker Aus. Vulgarisms [t/s] 8: drain the snake: To masturbate. [Hand-written MS addition: climb the wire, flog the lizard].