It's likely that Billy also survives in the talisman ending for the sole reason that he's friends with Nugget, and Nugget says that only Nugget and Nugget's friends live during the apocalypse. It would sure explain why there isn't an extra lightning bolt that hits Billy.
However, it doesn't explain why Lily is erased in this apocalypse.
Ozzy said that three of his friends were rezoned, and it's easy to assume that the three students you find in the lab are all three friends. However, one of them later says that she doesn't go to this school, so where's friend number three? Remember there was an extra monster: the one in the new Nugget Cave that Bob fends off. We see him at the end of the day, so we can safely assume that he won and that that monster was slain, doubly so since we don't see an extra student walk out. So Ozzy still lost a friend because of all of this.
After knowing how Bob is aware that there's a monster that he tried to fight off on Monday during Creature Feature, when you think back to the A Tale of Two Janitors mission, you might realize you've killed possibly humanity's last hope since the principal planned to take over all the other schools with mutated children. And Bob was the only one who was still aware of the monsters.
In A Tale of Two Janitors, when Penny dies from slipping on a car placed on the stairs, her entire head is missing. There's no fragments of it are there, just a bunch of green goo with her body on the ground.