Green’s Dictionary of Slang

domine do-little n.

also domini, domini do-little, dominie do-little
[SE dominie, a schoolmaster + do-little]

an impotent old man.

[[UK]New Brawle 5: [A] suck-egg, a askall [...] one who would rob a Hen-roost, rather than pleasure a Wife. Such feeble do-littles makes so many honest Women goe astray].
[UK]Spy on Mother Midnight II 39: Sir Domine praying very devotedly for Success to the Undertaking.
[UK]Grose Classical Dict. of the Vulgar Tongue.
[UK]Lex. Balatronicum.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue.
[UK]Vulgarities of Speech Corrected.