Lux was grateful to Cate for giving her a place to stay and for cleaning her wound but something inside Lux told her that Cate only did it because she felt guilty. That Cate felt guilty about the fact that the daughter that she gave up not only didn't get adopted but was also experimented on and got turned into a freak. As much as Lux tried to convince herself that it wasn't true her self-loathing made it impossible for her to convince herself otherwise.
Most would think that she hated herself because she was a freak. No, Lux hated herself because of her actions. There were things in Lux's past that she was deeply ashamed of and the thought of anyone finding out about them made her all the more ashamed. She had lived on the streets most of her life and had resorted to stealing, cheating, even selling herself at times. The only thing she was proud of was the fact that she had never sold herself for sex. It was a small drop of water in the center of burning flames.
Another thing she was proud of was that she had never used her special abilities on anyone that wasn't like her or Victor except Anderson. This fact led to yet another thing that she was ashamed of. The mistakes of her past kept whispering in her ear that whatever Cate did for her was either out of obligation, pity, or guilt.
Lux wanted to get close to Cate. She wanted to share the moments that she had seen on TV with kids and their parents. She had seen and she wanted to experience. She wanted to be able to sit down and watch a stupid movie with Cate and not feel as though there was an awkward pause or that she had to be careful of what she said or that Cate was being careful with what she said. She wanted to go out and be normal and come home upset and not feel stupid for wanting to cuddle with Cate and hear her say that everything would be fine even if she knew that things wouldn't be.
She hated feeling stupid. It was partly the reason why she didn't attend school all that much. She hated feeling that she didn't belong. She hated the fact that she wasn't able to express herself with Cate because she was too afraid of being rejected.
When Cate had wrapped up Lux's injury all Lux could think about was what she wanted and what she had missed out on. She had left immediately because she didn't want to reveal anything to Cate while she was so weak. Then she had felt compelled to thank Cate and it had almost come out then. Everything Lux wanted but felt too stupid, silly, and ashamed to admit.
She wanted her Mom. That was all she ever wanted. No matter where she was, what she was doing, or what was happening to her all she had wanted was her mother to come and find her and essentially save her.
Lux had been spiraling downward for a long time and she had done many things just so someone would step in and stop her but it had never happened. Instead she continued falling until she hit the bottom and now Cate was there and Lux was too dizzy to see whether she was there because she actually cared or if she was only there for a personal agenda. She wasn't sure if she would care if Cate was only doing it to ease some guilt. Cate was her mother. She had to love her right?
...right?