What was Cobra's thought process asking the Gorosei all this ?
The most logical conclusion the Gorosei would take from this is that his daughter or the entire family know more than they should and have a dangerous amount of curiosity.
Well Imu is interested in neferatiri family. With Imu looking at vivi's picture back then. Now coming in front of king cobra after hearing about lili. Lili might be Imu.( There are some other evidences in this chapter already pointing in that direction).
But if Imu is lili then why would lili kill her own descendent (or brothers descendent) cobra ? Why not tell her family that she is the ruler of the world. Why not tell her brother back in the day that she got a bigger job then being the ruler of a kingdom. Moreover what was written in the letter?( definitely not her appointment as the ruler of the entire one piece world). Why delete herself from the Alabasta history books ? This are the some counterpoints
Anyone dying at or returning from the reverie would make the World Government look bad so there was zero danger doing it here. The problem was Sabo and Imu, the Revs attacking gave the gorosei the opportunity to kill cobra and blame it on someone else especially after imu revealed themselves