"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.
Hey, Johnny! Have you seen Mugsy?" "Naw, he's on the lam for that caper he pulled in the Bronx