In the future, terrible chemical wars caused a bunch of 18 year olds DNA to be frozen, so they never age. They are referred to as "Freezers" but actually call themselves "The Lost" and live in the subway tunnels of a post-apocalyptic city called Obsidian.
They have been fighting with the city's dictator named "Falco". The Lost's leader is the main character named "Strat" who meets Falco's daughter "Raven" and it's love at first sight.
He pines for her, she pines for him, they can't be together, etc. During her 18th birthday party Raven admits to her parents she's in love with Strat, and Falco is enraged and says he will kill him if she doesn't stay away. However, her mom "Sloane" supports her.
Raven's parents (Falco and Sloane) are in a loveless marriage. Cue really epic rendition of "Paradise By the Dashboard Light" as they recount their teenaged lust.
After hours, Strat sneaks into Raven's room and they truly meet for the first time. And then run away together and drive off in Strat's motorcycle.
Partway through epic titular song "Bat Out Of Hell", Raven chickens out and runs home. Strat speeds up on his bike and crashes and presumably dies.