Green’s Dictionary of Slang

a mistress.

1610		P. Holland Camden’s Britain I 379: Edith his wife, who before time had beene one of King Henrie the First his sweet hearts and lig-bies [OED].
1629		R. Brome Northern Lasse V i: I’le be none of his Ligby for twice so mickle.
1667		J. Lacy Sauny the Scot Act II: He means to make one of your lasses his wench — that is, his love and his ligby.