Green’s Dictionary of Slang

1. (Anglo-Irish, also let off) a spree, an entertainment, a grand occasion.

1843		T. Haliburton Sam Slick in England I 267: Lord the first time I went to one o’ these grand let offs I felt kinder skeery.
1866		P. Kennedy Legendary Fictions of the Irish Celts 87: She went to New Ross to buy sugar and tay, and beef and port, to give a grand let-out to welcome her husband .

2. (US Und.) money from corruption.

1924

G. Henderson Keys to Crookdom 406: Graft. Money obtained through violation of a trust. [...] Protection, shake-down, let out, fall money.

3. an excuse, an alibi.

1954		‘Nicholas Blake’ Whisper in the Gloom (1959) 64: Bert perceived he had hit on the perfect let-out.
1984		Partridge DSUE (8th edn) 677: since ca. 1920.