In the story of "The Best Girlfriend You Never Had," analyze Lucy's relationship with men she dates and her parents in detail to give some advice about her relationships.

In the story, we learn that Lucy has had three boyfriends. They are Gordon, Jeffrey, and Josh. In addition to having had difficult relationships with men, Lucy also finds it difficult to relate to her emotionally distant father.
Let's start with one of Lucy's boyfriends: Jeffrey. Lucy dated Jeffrey because she believed that it would please her father. After all, Jeffrey had an MBA from Harvard, was socially conservative, and shared similar tastes in food with her parents. However, Lucy's efforts to please her father fell flat. When Lucy asked her father what he thought about Jeffrey, he replied insensitively that he had never liked any of her boyfriends and that he didn't imagine he ever would. Lucy also remembers with dismay that her father had cruelly asked her to refrain from asking his opinion about future boyfriends. Her father's rejection has fueled much of Lucy's insecurities about men. Because of her father, Lucy fears that she will never completely earn the respect and adoration of a man.
Another boyfriend, Josh, is mentioned briefly in the story. He is the boyfriend who "didn't want nearly enough" from Lucy. This may suggest that Lucy's relationship with Josh mirrored her relationship with her father. Essentially, Lucy seeks out men who are as emotionally unavailable as her father. Because of her low self-esteem, Lucy finds it difficult to develop healthier relationships with men. 
Her lack of self-confidence eventually turns off every man she dates. Another of Lucy's boyfriends is Gordon. Lucy tells us that Gordon earned his PhD before he turned twenty and that he managed to snag a tenure-track teaching position at Berkeley by the time he turned twenty-one. It is obvious that Gordon and Jeffrey share similar academic achievements. The text tells us that Gordon has a dysfunctional relationship with his mother in much the same way Lucy has trouble relating to her father. Both Lucy's father and Gordon's mother lack emotional intelligence; as a consequence, they relate poorly to their opposite gender children.
As the story progresses, we learn that Gordon harbors a "jealous streak as vicious as a heat-seeking missile." Like his mother, Gordon switches between moods effortlessly. On more than one occasion, Lucy relates how Gordon's jealousy often fueled irrational bouts of anger. During his outbursts, Lucy often found herself begging him not to drive away. As we read, we discover that Gordon's toxic relationship with his mother continues to fuel his insecurity. He admits that he fears being thought of as "weak and worthless." To silence his self-doubts, Gordon becomes as emotionally abusive to others as his mother is towards him: "I take the people close to me and try to break them, so they become as weak and worthless as me."
Later, we learn that Gordon slits the tires on Lucy's car, pours Karo syrup into her gas tank, rips one of her paychecks into a hundred tiny pieces, and destroys her box of Dylan's Biographs. Gordon's actions not only show a high level of self-absorption, they also demonstrate his acute inability to overcome his feelings of inadequacy. So, in order to live a happier life, Lucy must accept that she will never receive emotional validation from her father and that she must not seek acceptance from men who demonstrate the same inability to love. One can argue that Lucy would be better served to visit her father as little as possible or not at all until she can develop better mental habits. 
In time, as Lucy learns to accept her strengths and weaknesses, she will become healthier in her outlook and more scrupulous in her choice of boyfriends.