Green’s Dictionary of Slang

lettary n.

also letty
[Ital. letto, a bed]

(UK tramp) a lodging.

[UK]P. Allingham Cheapjack 168: They referred to these digs as their ‘lettary’. [Ibid.] 205: I had decided that none of us should be allowed to ‘scarper the letty,’ which means to sneak out of the lodgings without paying.