It is true Kallen is still not 100% trusted by Zero like CC is. But compared to last season, Kallen's making good progress. CC might be Zero's right hand, but Kallen is his left hand.
By no longer viewing Zero as a god, Kallen was able to stop putting him on a pedestal. The issue here, is that Lulu keep his plans secret not because he doesn't care about Kallen, but because he doesn't want others to share responsibility of the choices he made. If his plans messes up, Lulu would like to take the blame on his own. Lulu doesn't understand that Kallen has thrown her lot with him already, and want in as a partner the same way CC has become. Kallen want the responsibility of being Zero's confidant.
If Zero's a Warlock and C.C.'s a Witch, then Kallen want to be the Champion. Technically she is already in that position, but only physically. Lulu need to treat her like someone who watches out for him.