Why can't Lucy use sex to express intimacy?

Once in America, Lucy loses her virginity and has several subsequent sexual encounters with men and women. It is important to note that all of these sexual encounters occur without any binding emotional attachments. She emphasizes that having sex is not necessarily related to being in love. When she thinks her boyfriend Paul is cheating with her best friend, she claims not to care. In Lucy's journey to forge a new independent identity, she attempts to sever attachments rather than form new ones. Sex is simply an act rather than an act of intimacy.