She knew that the only reason she spend time with him 8 years ago was out of sheer boredom as a way to kill time before the Baskervilles find her. Lacie admitted to herself that she found Jack very strange. Jack was aware that he hated the impact Lacie had on him since he knew that he can't live without her. Due to her presence being the only way that Jack knows who he really is, Jack need her to be his side. Unknown to Lacie, while Jack's feelings seem romantic, it's actually more complicated. He seems to be in love with Lacie, but it's not known if she likes him back as she does admit that there was no point in loving him, and that she was going to die soon. He wished to meet her again and promised to never forget the name Baskerville. He loved Lacie very much after she saved him from being killed by traffickers. She even cut his hair to help him, and he still to this day kept his hair like that. She asked his name after introducing herself, and they spent a short while together. She was the one who found him in the alley on a snowy day. Lacie smiled to Jack in their first encounter. When she was 'cast' into the Abyss, she gave birth to twins, one of whom returned to him after the Abyss' power rapidly aged her, physically resembling a much younger Lacie. Later, it is revealed that he impregnated Lacie, as he asked her for her help in his experiment. Lacie may have some fear of Levi since she closes up or shows indifference whenever he mentions something that is personal to her. Although their relationship appears friendly, Lacie is shown weary of him during some scenes. It appears that he understands what she was going through with Jack as well as her inevitable death. It seems that Levi cares for her and occasionally removes her from the tower and takes her to the city, but often fails to do so. Levi and Lacie seem to have a decent relationship and some understanding of each other. It seems that both of them have an interest in Jack, although for differing reasons. The other when he watched her 'fall', he had a look of pain and despair on his face.
However it's shown that he cares for her very much, as shown when he was about to cast her into the Abyss and paused halfway through with a sullen expression. There are times when they fight and she runs away from home until he apologizes. They seem to be on opposite ends of each other. Spoiler warning : Plot or ending details follow.