Green’s Dictionary of Slang

(US) be quiet! shut up!

1922		T.A. Dorgan in Zwilling TAD Lex. (1993) 53: (OS: Talking about your boys progress in school now that the world’s series is coming on) Aw lay down Sisler will lead both leagues.
1933		Ersine Und. and Prison Sl.
1950		Goldin et al. DAUL 122/2: Lay down! (P) Shut up! Go to sleep (This is one of the most common expresions [sic] in prison slang.).
1977		E. Torres Q&A 69: ‘Horny motherfucker. Next thing, you gonna have your hand on my knee.’ ‘Aw, lay down, will ya?’.