Yeah. Klaus can't disobey her orders, but he's not actually loyal to her.

The Jaeger thinks it looks like what happens when the boss dies, but i don't think that's it, because Klaus is still very much alive.

Remember how each and every one of the "Specialists" Klaus sent into the city believed that they had been hand-picked for a very special mission. They Failed, so Lucy tells him to deploy his regular troops.
He gives each commander contradictory orders, and tells each one that he has elected them, personally, for this very important task.
Perhaps he even gave each one a "Secret Mission", ordering them not to tell anybody else about it.

Puffed up with their own importance, each commander arrives and finds themselves faced with countless OTHER commanders, all of whom have equally inflated heads.

Meanwhile, Boris and others should be realizing that something is very, very wrong.