I think this is a lazy behavior of the author. He is eager to promote the plot, but the details are not perfect.
Actually, Rena doesn't need to mention laki to Zetou,Therefore, laki was not scolded by Zetou,Laki won't attack her and introduce her to work.
The reasonable plot should be that there are two routes: ① you can choose to tell Zetou the truth and become his false girlfriend; ② you can choose to hide the truth and rely on laki for his help, but you need to be his real girlfriend. Laki can make Rena a performing artist or something. Whether relying on Zetou or laki, she can get money to repair the combat uniform and complete the task.
But the author should think that it is difficult to achieve,He deleted it.