I'm on my third playthrough, and in both my first and second playthrough I was not able to plough the goddess, but I know it can be done.

Does anyone know how to enjoy the lady's company?

I think the prerequisite is to talk to her enough to trigger the advice to go talk to the Hermit about the Holy Grail, than talk to the Hermit, who has a lot to say about it.

Return to the Lady and announce you are going off on a "mission of paramount importance." Then immediately admit it was "a jest". After some banter, you will seduce her by paying her the right compliment.