Of course, Axel himself could isolate that with his own mana, so that it would detect no changes in the surroundings, Lucien would realize he had been compromised sooner or later, and Axel didn't have that patience. Lucien needed him because his value was increasing as an individual asset day by day; as such, he couldn't do anything to disregard him. The reason why he instantly destroyed it was clear: it was a warning not to ever do such a thing again.
Axel would not be taken seriously if he continues to compromise, because no matter how intelligent Lucien thinks he himself is, as a dragon bloodline holder, he unconsciously values those people more who hold more strength, and he does not even realize that fact.