While Lucifer was watching the show between them, he wasn't just idling around. He ordered his subordinates and followers to start making their moves.
Since Wrath is busy right now fighting, he shouldn't be paying attention to what is occurring in the other layers of Hell.
So, Lucifer made preparations before he came here for his subordinates the Dukes of Hell to start eating the territories that belong to the Sin of Wrath in the other layers.
In the past few months, he has been moving cautiously to not alert the other Seats, but everything changed in the past 4 months.
He received help from some suspicious origination that told him that they will help him achieve his goal.
Although suspicious, he gladly accepted their help since they only have a verbal agreement and no Soul contract.
He will only use them and then discard them completely. He has no intention of playing into their hands.