"Leeze me" is in Chambers's Scots Dictionary, with a ref. forby to "Leese" -- John F has it right: "lief" is an old-fashioned sort of word (entirely obsolete in English) meaning "dear"; so "lief is me", shortened to "leeze me" or however you want to spell it (using the ethic dative, I suppose you could say) means "I hold dear", "I'm fond of", etc.
"Jacob Curate" adds that "This whole story is as well known in Scotland, as that the covenant was begun and carried on by rebellion and oppression". As for the date, it precedes the book date by quite a few years. There are other remnants of the scurrilous tale--in Maidment's "A Packet of Pestilential Pasquils" (limited appendix to the 1868 edition of "A Book of Scottish Pasquils 1569-1715), p. 24, is a satire (one of many) on Williamson (no. X, 'Elegie on the Death of Williamson. By Mr. Finnie'), which contains the lines

Ladies, with brinish tears bedew your cheeks,
Ye've lost the three considerables in his breeks.
I cannot comprehend his praise in verse,
For Cherrytrees hath aggrandized his tarse,[= prick]
So that in Venus' field he led the van;
And Charles desired to see this able man,
While in the oak, tho' he had a great soul,
Had neither heart nor hands to wiled his pole;
But he in hazard of life at Cherrytrees,
Was bold to enter 'twixt the ladies thighs.[etc.]

Maidment notes: "Charles the Second was so much astonished at Williamson's prowess, that he sent for the divine when in London." Williamson married his seventh wife, Mrs. Jean Straiton, on 20th May, 1700; he died 6th August 1706.