Rudra was in a tough spot with Lucifer , as he knew he needed to have a valid reason for being in the posession of the pages from the Demon's diary and he could not lie his way out of it.
But the valid reason that he had to be in the posession of the pages was that he was a reincarnator and had knowledge about how the pages were a part of the main storyline of Omega.
It was not something that Rudra could explain , as although he indeed had posession of a lot of pages he had no idea about how to use them or what part they served in the main storyline. However considering how Lucifer wanted them soo badly , it was surely not something simple.