Green’s Dictionary of Slang

(orig. milit.) a latrine.

1940		M. Marples Public School Slang 112: LAVATORIES [...] rears, lats, shants.
1941		G. Kersh They Die with Their Boots Clean 92: If you’re going anywhere at all, even to the Lat [...] you’re supposed to take your respirators.
1946		R. Rivett Behind Bamboo 397/2: Lats, latrine.
1963		C. Wood ‘Prisoner and Escort’ in Cockade (1965) I iii: Lats.
1983		(con. 1940s) D. Nobbs Second From Last in the Sack Race 183: He died sitting on the outside lats.