"Professor, I'll keep watching the Diary for a while. We only need to make sure it lures or controls Lockhart into opening the Chamber of Secrets..."
Although Dumbledore was not certain Will's deductions were correct, he still let him proceed. They had to investigate the chamber themselves to learn what was truly inside.
Only then could Dumbledore ensure that no one would enter it in the future and become another calamity because of its wicked knowledge. Destroying the Horcrux was his goal, but so was finding the chamber.
Will's plan was to monitor the Diary and Lockhart, then follow them down when the Diary took Lockhart into the chamber. Meanwhile, Dumbledore would hold back, secretly guarding against the basilisk.
Next, Will would "reveal his ambition" and force the Diary to divulge the secrets of Horcruxes and open the true chamber. That would accomplish both his and Dumbledore's goals.
After they settled on the plan, Dumbledore even enlisted Snape's help to make Will's "disappearance" more plausible, spreading word that he had suffered an accident while brewing a potion and needed treatment in isolation.
This gave Will ample time and a reasonable excuse to watch Lockhart, though he would miss classes for a while—not that the Second Year curriculum meant much to him anymore.
Will borrowed the Marauder's Map from the Weasley Brothers in exchange for some startup funds to support their business.
At Hogwarts, with the headmaster and a professor supporting him behind the scenes and the Marauder's Map in his hands, Will had everything he needed. The Diary and Lockhart had unwittingly become ensnared in the net they had laid.
Today, their plan had succeeded spectacularly. Dumbledore had achieved his goal and discovered the true chamber.
Will, too, had reaped enormous rewards. Under their agreement, all the knowledge Slytherin had