Before Laksh made his promise to DP
I would like to discuss about what Laksh would have done if he knew about Swara's feelings before DP's announcement. Some may feel that he would have left his house for her. But, I think he would have been rather forced to leave the house by DP. Laksh loves his parents too much to say that " Look I love Swara and she loves me. That's all I need. I know you won't accept her. But you know what I don't care. I am out of this house." He would rather try to convince his parents but after seeing that DP is pretty adamant, he would get upset and might get into a heated argument with his father. Then, DP will announce that he will have to forget Swara if he wants to live in Maheswari house or else he can leave the house forever. Obviously, Laksh will decide to leave the house
After the promise
But, I think the situation would have been different if he realized Swara's feelings after the penance segment. Yeah, He made that promise to his father because he was sure that Swara will never love him. But, that heartbreak also gave him a better understanding about relationships. Remember his warm conversation with his dad. He even said that he now understands that DP mush have gone thorough the same pain they all went through when he had to throw Sanskaar out of house. He began to understand his father better and their relationship became stronger after that incident. He also told Swara during the kidnapping segment that even if she says yes, they cannot be together because he has given his word to his father and he wanted to meet her just to say this. So , I think if he realized that Swara too has feelings for him, he would have definitely tried to convince his parents but would have taken care not to hurt them as well. After all, there is enough power in his love for Swara to convince his parents he can be happy only with Swara. Would love to hear your thoughts