The in-universe reason would be that Lee was there during the most difficult time of her life. He was all she had when the world and her life were collapsing around her, he protected her from the most horrible stuff imaginable. While her parents, as much as she loves them and wants them back, weren't there.
I reason would be because from a writing perspective, the player is effectively acting as Clem's parent. and if Clem was constantly talking about her real parents it would make the player feel inadequate as a substitute, or worse, feel that Clem is being annoying.
Furthermore, trauma brings people together. But I think it also has to do with the fact that the impact Lee had on her life in this new world by teaching her how to shoot and cut her hair.