Many Lan Shang x Shi shippers out there often mistaken Lan Shang as the person closest to romance for Shi. She is not. Unlike Yan Da, Lan Shang was not even a friend to Shi. She was merely a pawn. Let me explain this in detail.
1. Everything that Shi did for Lan Shang was all to protect Ka Suo in the end.
2. (Book version) Shi first saw Lan Shang in her human form (mermaids turn into humans when they reach adult age) when the Ice King introduces her as Ka Suo's fiancée. Shi told his father to give Lan Shang to him, not because of love at first sight, but because he knew that Ka Suo was in love with Li Luo. Since his magic was the most powerful, he told Lan Shang to marry him so he could protect her. Otherwise, if she chose Ka Suo, Shi can kill her whenever he wants.
3. (Drama version) After becoming the Ice King, Shi offered to marry Lan Shang several times but was always turned down. He did not do it out of sympathy or love. He only did it because he was afraid that she will ruin Ka Suo and Li Luo's relationship. Shi did not want Ka Suo to feel guilty or burdened for not taking the throne and marrying Lan Shang.
4. (Drama version) When Lan Shang asked Shi if he loves her, he said he will try to. He was only forcing himself to do so because he wanted her to get away from Ka Suo.
WARNING: HEAVY SPOILERS AHEAD. DON'T READ IF YOU HAVE NOT SEEN KA SUO AND LI LUO'S WEDDING.
5. (Drama version) As I said
before, Shi's cold and ruthless personality prevented him from having emotional attachment towards anyone besides Ka Suo and his mom. Therefore, when he felt bad about failing to prevent Lan Shang from getting defiled by Shuo Gang, it was because it would make Ka Suo feel guilty and sad. Same reason applies to her suicide. Some people may argue that he felt sympathy because of morals, but I think it was only due to his respect for women like his mom.
6. (Book version) Did you know how ruthless Shi was in the book? Since Lan Shang was an eyesore, Shi defiled her. This drove her to suicide because having her legs turn back into a tail, meaning that she was defiled before marriage, was a humiliation.
7. (Book version) Li Tian Jin even mercilessly slaughtered Li Jing, who was Lan Shang's reincarnation and Li Luo's lookalike.