as far as the clock and box youre saying are a little not accurate, l'll explain what happened in the anime at the end from my standpoint
Lucy and Nyuu are one and the same person, however Lucy is the Violent Victim while Nyuu is the Gentle newborn life that was given to her when she met Kouta in the past, for some reason he didn't resent her being Diclonius, he was very kind to her, thats how Nyuu was as well, when Lucy arrived at the beach when she broke out from the facility, wich was an epic episode so to say, it was a laugh from fate that he was there, she didn't even need to look at him, she recognized him instant she heard his voice, and collapsed, however her mind needed to function for the time being as she hid herself and gave surface to the gentle side of Lucy that she learned in the past from him, by the end of the anime Lucy and Nyuu have a talk in their mind, and at the final Lucy's music box stopped showing she decided to stop the old Lucy stuff, being the victim all the time has worn her down, she had enough of this, and the clock started working wich represented the other side of Lucy, the one thought to her in the past, Lucy as Nyuu and Nyuu as Lucy became one person, they both loved him deeply, but probably would never bear to again see his face from the guilt of the past, however that scene represents that they both will from now on move on, Lucy will no longer be a victim and the embodiment of violence, and Nyuu will have grown, they both merged and now go into the world to experience it as a newborn, after all, noone will be able to tell shes a diclonius anymore, she lost both horns, no one will resent her, no one will hate her anymore, she was given a chance by fate, and shes willing to grow anew.
that is my point of view at the ending in the anime, l bet if we could we would see Lucy walking away both crying and wit ha smile, crying for leaving the one she loved, and smiling for welcoming her new life.