From my understanding of the law a person sentenced to life without parole can appeal the life without parole sentence.
But the prisoner sentenced to life without parole only has 30 days after sentencing in which they can put in an appeal for the life sentence.
After that and if the first appeal is denied for the life without parole sentence then the prisoner will remain in prison until they die.
They will not be getting out of prison unless they die and come out in a body bag so they'll be spending the rest of their lives behind those prison walls.