Green’s Dictionary of Slang

to have sexual intercourse.

1688		C. Sackville ‘A Faithful Catalogue’ in Lord Poems on Affairs of State (1968) IV 209: Haughty Di in just revenge will lig, / Although she starve, with any senseless Whig.
1725		View of London & Westminster (2nd part) : [in a list of prostitutes] Miss Lig-close [Is Visited] By a Sc. Nobleman.