When they first met, Lucretia commented on how similar Godou was to his grandfather. She later referred to him as a toy for her entertainment, even going as far as to give him the Prometheus' Grimoire just to see if something interesting happens. After Godou became a Campione, she went about picking on him and seducing him. She calls herself Godou's 'foreign wife.' Whether this was out of genuine attraction or simply having a bit of fun remains to be seen.
Lucretia and Erica are like-minded in that they both enjoy teasing and manipulating people for their own amusement. She even helps Erica trap Godou in Sardinia during the summer, suggesting they get along well enough to cooperate.
Due to the fact that Yuri is such an innocent girl, Lucretia can't help but tease her. She has been known to "teach" Yuri about men in a way that "just happens" to make Godou look bad just to see their troubled expressions.