Green’s Dictionary of Slang

1. (US prison) Leavenworth Prison, Kansas.

1970

‘Red’ Rudensky Gonif 6: I was broke, back in stir, and the Big L was surrounding me.

2. (UK prison) a life sentence.

2004		(con. 1980) N. ‘Razor’ Smith A Few Kind Words and a Loaded Gun 234: Though I might act tough on the outside and pretend that if my time came to get the big L, I would shrug it off, privately, I was shit-scared of going to prison for life.
2008		S. Ferranti Street Legends n.p.: Gangsta’s don’t live happily ever after. They die viciously or get served the Big L, a life sentence in prison.