Overly Suggestive
Landlords have superiority when it comes to the relationship between them and a tenant. Therefore, a certain type of professional dynamic should be maintained between the two. This sleazy landlord waited until right before his tenant was moving to make an overly suggestive and very inappropriate invitation for her to live with him.
Assuming it was a joke, the tenant played along asking if the rent would be free. He said it would be free of monetary charges but she would have to show gratitude in other ways. You can probably guess what he meant by that. Following up with the statement that she’s beautiful made her sick to her stomach.