L knows how it sounds; he had been skeptical, at first, but on the other hand, trusting his gut has rarely led him down the wrong path. Usually that was all due to the mistake of trusting other humans.

"I see... that one shouldn't be too difficult. To get started, what's your name, omen, and Patron Pthumerian? If you know it."

It's unclear, really, whether or not L needs this information to find the book, or wants it for his own reasons. Either way, he waits expectantly for an answer.