Of course, Lyca didn't listen to Santa's advice about laying low. When the King is ill, isn't it the Queen's job to calm down his subordinates? While Lyca wasn't in the mood to actually try and talk to more people, she thought it would be good to solve one more problem before going to see her husband.
And it was to settle something inside this Q Tower.
After Lyca went to see that old man Rolio or Ghost Rider and knew about the Q Tower, she immediately asked Ronan about this tower, and realized that this wasn't really some literal tower that was on her mind. And Shen Qui didn't create this tower— he stole it. Well, stealing was not really the right term as Shen Qui killed the previous leader and became the new leader.
