I've wanted one for a while. Would take a lot of work to implement at this stage in the game though, but it'd result in a ton of people going back to earlier areas for the sake of filling it out for completion purposes. The earlier they get started on it, the easier it'd be to work on in the long term.

Unlocking entries would probably work quite a bit like a hunting log, but with some differences depending on the type of content.
- Regular monsters out in the field need to be defeated 5 times to have their lore entry recorded. 20 times for stat and attack descriptions.
- B, A, and S rank hunt mobs need to be defeated once to have their lore entry recorded. Three times for stat and attack descriptions.
- FATEs only need to be cleared once to be recorded. I was thinking there should be more, but there's more than enough FATEs on ridiculous respawn timers already.
- Dungeons need to be cleared once for a general lore entry, twice for lore entries on basic enemies in the dungeon, three times for lore entries on the bosses, four times for stats on the basic enemies, five times for boss stats.
- Trials and 24-man raids work similarly to dungeons, but omit the 'basic enemies' part since everything would be treated as a boss, meaning you only need 3 clears to count for total completion.
- Let's include Diadem in there too! Mobs behave as regular monsters. The only FATEs recorded would be for the boss FATEs (and the Blood Wings FATE, which is technically a boss on a shorter timer), and they would behave like a hunt mob. The Emergency Mission entry would behave as if it were a Trial.

Oh, and filling out entries should award you EXP, just like the hunting log. There'd be a large EXP bonus for filling out all 'lore' entries within a particular area, a title for filling out all 'stat' entries, and maybe a piece of related glamour for total completion of a zone (like a wreath crown similar to what the Moogle King wears for completing all Churning Mists entries).

Should probably exclude quests though, it's really just a lot of extra work for something you only do once. Most important quest NPCs you fight would already be covered in the lore book too.