Lance doesn't seem to care but he does care a lot, he cared when she got drunk and was left alone at Rendezvous. He cared when she was caught by Jacob drunk with him in front of her apartment. He was worried that Jacob would be angry with her and would punish her. He cared when he saw her drinking at the hotel at Mt. Celandine. He can't even be at peace so he went back to check on her only to find out that she was missing. He was so scared when he couldn't find her and when he did, he felt his heart was pricked with a thousand hot needles when he saw her crying. He was never scared like that before, he never felt like that before.
He doesn't seem to care when she starts avoiding him but he does care. He doesn't show it but he becomes frustrated and ill-tempered, that's why he visits the filming set much less. Because he doesn't want to be disappointed when Lily avoids him again. He cannot take it.