To be honest, that was something which also bothered me when watching it the first times. Why fire him just for asking this single question? But it certainly makes sense, even if probably not written that well:
Fox has always been a thorn in the eye of Earle, who banished him into the dead end the R&D department is (or was). So when going to him he just needs some information about this emitter. But Lucius asking this slightly curious question ("you don't miss one, do you?" or something similar) was probably a bit too much for Earle's nerves at this point and he probably also interpreted a bit of a spitefulness into this question (which might even have been intended by Fox). So at this point Earle was just too fed up with Fox and did what he was going to do sooner or later anyway.
EDIT: And as Morpheus adds in his comment, Fox also makes a good scapegoat to blame for the loss of such a valuable R&D item.
