In Mudcat's QuickLinks dropdown menu, we have a Scots Glossary that may be helpful to you.

I interpret "For noo I lie wi' this ain until the day I die" as "Now I lie with 'this one' until the day I die." In other words, he chose somebody else, and he's stuck with her for life because they got married. And the term "this ain" implies at least a modicum of disdain, and regret for having married someone other than the partner of one's dreams.

The song is Roud 21824, which has three entries, all recorded.