Green’s Dictionary of Slang

anyone mild, pleasing, amicable; often used by women of malleable men.

1874		F.C. Burnand My Time 95: He’s an elegant Baa-lamb, and you’ll meet him at dinner.
1914		E. Dyson Spats’ Fact’ry (1922) 59: Tiger gets down meek as a baa-lamb, ’n’ swears off the game on ’is bloomin’ oath.
1915		Hargreaves & Godfrey [perf. Ella Shields] Oh, the baa-baa-baa lambs 🎵 Oh, the baa-baa-baa lambs, there they are, la di da / Twenty up to forty, looking a trifle naughty.
1956		Wodehouse French Leave 206: ‘Jeff’s a baa-lamb.’ ‘He’s a nothing of the kind. He’s a wash-out and a broken reed.’.