He's going to set that Eck guy up, isn't he? Trick the man into thinking he has the upper hand and have him attempt prove that Satsuki's version is fake, which actually results in proving his own deception and him making a fool out of himself in front of the representatives.
Furthermore I suspect that Satsuki's version will likewise be proven fake (and that there is no real Will), but that either Luke, Yuuri himself, or both will step up and declare that Luke will agree to be the interim Family Head (since Satsuki already got permission from the Queen for that and Luke can easily get certification) and Yuuri will take over the position upon graduating from the Academy.