This lesbian tryst theory was pretty much entirely conjured up by Ed McBain (a.k.a Evan Hunter) in 1984, and there's very little support for it: https://www.straightdope.com/columns/read/1894/did-lizzie-borden-kill-her-parents-with-an-ax-because-she-was-discovered-having-a-lesbian-affair/. Seems a thin and controversial argument upon which to base a movie.