Sure, but the Klingons present were the ones she needed to convince that she was her own woman. Now, not only did she lie to them but the question of whether she's a Federation puppet is alive again.
Read what I added in afterwards. I think they benefit more from having L'Rell in charge than someone else. Why? Who knows. Some of them also just might not want to be #1. If you're a lesser target, you won't be the one everyone's after.
For all we know, the Klingons on L'Rell's ship are the only ones who know about Tyler.