Emet just calling Lahabrea an idiot does come off a bit strange after Shadowbringers, probably because even at that point they were still nailing down the details of everything for the expansion. But I think its more or less workable. Going by the short story, both him and Elidibus expected Laha to get himself killed eventually, they have really hammered in the lore that he was the one who deteriorated the most, both mentally and in power.

So Emet being so flippant about it is probably a mix of Emet having had centuries of expecting this very thing to happen, him trying to bury his own grief, and probably on some level at the very least just a little bit of genuine resentment bleeding through. Resentment of his peer for not holding it together like he had through all the Eon's. Leaving him more or less carrying all the weight himself.

Really, the more we learn about the Unsundered, the more it reads like alongside everything else, Emet had to spend a significant portion of time playing some manner of care taker for the other two. Having to work to keep your two mentally degrading comrades on task for Eon's would take a huge toll on anyone.