I think that the whole suicide thing started with Judas and because he is lost we believe that any person commiting suicide is also lost, but I believe that Judas did not make it not because he committed suicide but because he did not believe that Jesus could forgive him.Peter betrayed Jesus three times, Judas only once,but Peter believed in the Lord's mercy,while Judas did not, otherwise he would have done the same as Peter.
Let's say that a mentally ill person, that is not responsible for his actions, commits suicide.Who is to say what will happen to that person?
I don't know, all I know is that God knows better!