I sense a bit of possible irony here. Could it be that she told him that they were going to be eternal lovers in death, and that he needed to kill himself first, and that she would then kill herself? Possibly in an attempt to be rid of him?
And then, he shoots himself, but survives and kills her instead? I wouldn't put something like that past some women out there...
They should have put their heads together and then the gun to one side. From what I read its like he had his head on her lap and he tried to kill himself.