Treyton and the others were apparently already assigning Vivi and Lex to their subteam. They were already done with their introduction to other members.
Luciel already knew about them, and the two also knew him, so Treyton didn't need to introduce him again. Luciel also just focused on eating while listening to their conversation.
They had decided that Vivi and Lex would be assigned to Zam's team because Wes' team had more people before, so they had to be assigned to Zam's team.
However, the two of them were still training with the military every afternoon, so they wouldn't be going on Zam's mission the next day.
Treyton let them continue training with the military, and they also had to train in the morning because they're not strong enough yet compared to the other members of the team.
As for their living quarters, they had to live in the apartment building with Dan and the clothes because there's no more space for them in the villa area.
