Trying to keep all of the politics togther lol. Rereading chapters 22 and 23, all the way back to when Alexandra was transferred to Diana's team, Lapis wanted to instigate fake rumours. By having a noble transferred to the commoner's team, it would seem like they were purposefully sabotaging their victory if she threw indiscreetly. However, Lapis' objective was irrelevant whether the team lost: if Diana won, it would give commoners hope. If she lost, then the rumors would spread either way.
Either way, Lapis sends Rubeus to canoodle with the anti-royalist nobility faction. Meanwhile, Diana will become a figurehead for the commoners. Lapis believes that the ARNs are being silly (they are), because using the commoners' anger to stage a coup will, in fact, not solve the fundamental issue of class divide. The ARNs will attack Lapis at some point. If she can reveal the ARNs' schemes while being presumably an innocent bystander, then people will naturally denounce them and hopefully topple their leader.
One thing I hesistate about is her final goal: kingdom preservation. If Lapis dies, it won't quench the commoner's anger, but it will rouse some sympathy. If I were a commoner, though, I'd probably just go, "Well, that sucks. Even the system is unfair to some rich people, huh," and shrug it off. I guess Lapis doesn't really care about upholding the nobility system, so far as "I hope these commoners don't just rip the whole kingdom in half," like France's Reign of Terror. She does want the stage to be theatrical, so perhaps her death is so shocking that it resembles Joan-of-Arc on a stake level. People are so horrified by the manner of death that they would have no choice but to be reasonable.