Multiple “life” sentences affect parole, pardon, and commutation decisions, and if one conviction is overturned the other may stand.
I always think of Richard Pryor’s routine...
“How do you do ‘Triple Life’, that means if he die and come back, he gotta go to penitentiary.”
“____ Kindergarten, get your ass back to the penitentiary....You know what you did last time you was here!”