While Ozymandias was meeting with Luthor, two other iconic characters were meeting for the very first time.
Ozymandias had deduced that the smartest man in New Earth was Lex Luthor. However, he would be remiss if he overlooked its second smartest man, Bruce Wayne. And the job of tracking Wayne down went to the new Rorschach.
With Bruce away dealing with his aforementioned issues with Gotham's new feelings towards Batman, Rorschach sneaks into Wayne Manor, eats the pancakes that Alfred had left out for Bruce, and quickly comes across the Batcave.
From here, we get a fairly deep sequence of Rorschach exploring the cave, during which he comes to the conclusion that Wayne is some sort of monster, even comparing him to the original Rorschach, Walter Kovacs. He calls attention to the fact that they are both incapable of letting go of the past, citing the various "trophies" Bruce has collected from the various criminals he had defeated as Batman over the years.
However, on his way down into the cave, Rorschach had tripped the silent alarm. And before long, Batman had returned home to face down the intruder, leaving the two standing face-to-face as the readers are left to wonder exactly how the rest of this interaction will play out.