they are the dukes of one of the 4 direction i dont remember the cardinal direction so they hold a lot of sway with everything. and plus the empress is also the one that is holding the region and empress regent of her son ( if he ended up being the emperor ) . they are also the second welthiest in the country too. so in a sense, as conniving as they are, people are willing to gamble to be her ally or in her good grace as if the throne is pass down to her son. she will have the central and one of the region in her power thus making the power balance tips heavily in her scale.

Maybe, just maybe they don't like Lombardi, or they've been "rejected" by Lombardi in a way or another. Or maybe their family has been in the same fraction who supported angenas since before the empress became empress. Or maybe it's easier to accumulate wealth and influence when one is siding with angenas even though they know they're bad people. Or maybe like the other comment said, they're trying to get into the next emperor's good grace, assuming the first prince will be the crown prince. Or maybe they just simply stupid. Or maybe the devil's side is more tempting than the angel's side. In the end of the day, it's politics.
Reading my comment again, I didn't answer your question. Sorry. I'm too lazy to delete them. But imo angena and Lombardi was almost in the same level; wealth, influence and power wise. It's justthat the angenas seem to have too many malicious people and being lead by one cold hearted and mean person, whilst Lombardi's head is someone wise who tried everything to keep the next generation in line

Maybe because the emperor favors them (I think) and they threaten a lot of people (mostly the poorer ones it seems).