He now learned exactly the opportunity Loki was cueing him for.
As the absolute God of magic—and trickery, the opportunity Loki was showing him definitely revolved, around that area. Now that he had learned the broader picture of Thalia's situation, he realized what needed to be done.
Or rather, exploit.
Knowing how Professor Fury, fell in the direction of the Crimson Wolf Clan, the clan must be very influential to make a professor commit a crime on academy grounds, and as the rival of that clan, the Green Tempest Clan must also be close to that level.
From Lucivar's perspective, this is a big opportunity for him to grow stronger.
Where there's chaos, there's opportunity.
If two packs of wolves are fighting, the Beta who guarded the cubs will share the glory.
Lucivar could gain a lot if he positioned himself in the right place.
But in order to do that, he needed the full trust of both Thalia and also her sister, Elira.