You're alternate persona may be a way to escape reality. I understand that you've had a female orientated family and maybe you always wished you were a girl to try and be in competition with your sisters and make things easier for your mother? Another explanation may be that has anything happened when you were younger? Maybe something altered your personality and you don't remember this as you have repressed this memory? I think you have a mix up of gender identity. Are you happy being male? Or do you wish to be a female? Gender dysphoria may be a suggested problem - but i think gender fluidity is also viable. This can also be a symptom of Schizophrenia - not saying that you are, but it may be helpful to get it checked out?

I recommend you try and get some psychoanalysis done, just to check if there are any repressed memories, and where this "Lisa" actually came from and why she is staying there. From actually creating an alternate ego, and believing that you're actually them has a big development process - therefore at the start i said you may wish to escape reality? You say Lisa appears when you're alone, maybe you have anxiety? And you feel that if Lisa is with you, you have someone to console in and a bit of company? If you wish you to talk this further then do pm me ! I'm no expert in this manner, but it might be useful to try and understand your problem and see if there are any options to sort it out.