I know Mello wrote Another Note: The Los Angeles BB Murder Cases after a conversation with L, but to my knowledge, we don't exactly know how this conversation was had. I somehow don't believe L would have visited the House just to talk to Mello, and somehow, even a phone call seems a little bit too extensive for someone like L to conduct for such a discussion. I imagine he and Mello sent several very long emails to one another, in which Mello flooded L with questions, and L answered them as succinctly as he was able. Mello would sit at the computer for hours, rewording his questions and deleting large paragraphs under the illusion that the detective had far better things to do than respond to him, especially given the tone of his responses.
What he didn't realise is that L would see these emails and always stop what he was doing to read them twice over, three times if necessary. He would tell Watari to reschedule any appointments he might have had and carefully word each sentence in a manner he thought would be as efficient as possible, so that this young successor of his wouldn't find the story tedious. He always found Mello's enthusiasm, all too clear in his queries, to be rather endearing, and for a brief time felt as though his work was interesting, as frustrating as it could often be.
The last email was sent by Mello, no longer interrogating L over the case as he felt his responses had been sufficient for him to begin writing his book. He had documented all that he needed to know, and had broken into a file cabinet in Roger's office to retrieve additional information about Beyond that either L would not have been aware of, or felt inappropriate to explain. Instead, he thanked L for his time and told him how hard he was working to be worthy of his position, eventually. He couldn't have been more grateful for the opportunity to follow in his footsteps.
L didn't reply, not out of lack of trying, but he could not bring himself to warn Mello of what his role really comprised of. That to be L was not an enviable title, and that he would only find pursuing such work disappointing and meaningless. As such, the email thread was concluded, and the next time Mello heard of his predecessor's condition, it was in Roger's office once it was confirmed that he had been killed by Kira.
