Cutlife, I do not have the answers for you, but I can relate and only share my experience and maybe there is something you can use.
I have not been diagnosed with DID. My therapist said she is "cautious" to give that Dx. But she did say "splintered personality". I sleepwalk. I have "dreams of three of me".
I am currently married to the best man I have ever known. He is wonderful. When we first started seeing each other, I was scared to death. I had been divorced for 3 years and had been married 10 yrs prior to divorce. My 1st husband was very abusive. I was terrified of falling in love with my current husband. It did cause some stress, but nothing I could not handle.
Shortly after we moved in together one of my "splinters" confronted him. I call her Tiger Lady...idk her name. He told me about waking in the night and moving across the bed like a "big cat", very seductive and sexy...but i have no memory...still. She was very aggressive and tried to scare him. I think she was trying to get rid of him. He laughed at her. She went back into hiding. As far as I know he has not seen her since. But she was trying to protect me. I had not told him about the three of me...he told me. I had never told ANYONE about Tiger Lady...she lived only in my "dreams".
What i think is Lisa is scared to death and trying to "protect" Melissa. But it is a decision for Melissa to make.
Does Melissa ever communicate with Lisa? Maybe that is what is needed? Please do not give up. Melissa deserves to be happy and Lisa is just terrified that she will be hurt. And if Melissa gets into a safe relationship, she may not need Lisa as much and that is where Lisa is coming from. As long as Melissa is in an abusive relationship, then Lisa is her protection. If she has someone safe adn protective, other than Lisa, this threatens Lisa's role.
I am not sure if my rambling helps, but there it is, lol. I wish you guys the best and much happiness. Oh, there is probably no way to win Lisa over. Not at this time. That will only come with time....probably. But no matter what resolution you guys come to, Melissa needs you love and support. When we have been in traumatic situations and abuse for a long time, it is what we know and "normal" is scarey and confusing. But it is a beautiful thing when we adjust...
Mush support and hugz...good luck...