on the lam

みました。　今日取り上げるのはその中にあった慣用句です。
Ichihashi also comes clean about his attempts to change his appearance, including sewing his nose with needles in a public lavatory on his first night on the lam.
容疑者の市橋が逃亡していたのは知っているので、 "on the lam" は "on the run" と同じ意味の様に思えますがどうでしょう？　辞書を見ます。
・Dictionary.com: escaping, fleeing, or hiding, especially from the police: He's been on the lam ever since he escaped from jail.
・Cambridge Idioms Dictionary: running away from the police or someone in authority in order to escape going to prison He finally gave himself up to the police after 12 years on the lam
また、Wikipedia の "fugitive"の項に次ぎの様な説明がありました。
"On the lam" or "on the run" often refers to fugitives. Mencken's The American Language and 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. Mencken quotes a newspaper report on the origin of 'lam' which actually traces it indirectly back to Shakespeare's time.