To be running away from the authorities. This term dates back to the 1920's and was a part of urban slang.
"I pinched the hooch from some drugstore cowboy of a raggle-muffin and now im on the lam so you better scram or ill knock you off. Kepeesh!"
by Brian R. Turner September 26, 2006
"On the lam" or "on the run" often refers to fugitives. The Thesaurus of American Slang proclaim that lam, lamister, and "on the lam" — all referring to a hasty departure — were common in thieves' slang before the turn of the twentieth century. A "lamister", or, "lamster," is a slang term for fugitive.
by antkneep June 28, 2011