With Luciel's personality, Treyton knew he probably didn't mind being known to the base. However, he would surely mind if he was disturbed because of them.
Luciel didn't care much about what was happening around him, as long as it wasn't too big of a matter or didn't concern him directly.
That's why, even though Treyton had already given enough authority to Luciel, having ordered that if he wasn't around, the others could follow Luciel's orders but Luciel didn't really use that authority. He only used it when he gathered everyone to plan something fun, like the pool party.
Aside from that, Luciel didn't bother others at all. He really didn't seem to have any interest in taking charge of the team's affairs, even though he was clearly very capable.
