I don't think we need to update the FAQ. If question about "plot and characters" being on-topic isn't going to stop close votes, I don't think adding the word "lore" in there is going to change anything. Most "lore" questions are actually about plot and characters anyway.
As others have mentioned in comments, I also don't think a lore tag will fix any problems people have with these questions and stop them from (usually incorrectly) casting close votes. As for downvotes, they're free to downvote as they wish, whether or not a category of question is on-topic. The only real utility I can see for a lore tag is that it would give those who wish to ignore such questions the ability to add it to their ignored tags.
In my experience, most of the close votes on lore questions aren't simply "because they're lore", but because they have other issues, like speculating wildly about why things are the way they are or what would happen if they were different. That's more or less what this entire meta question is about. And despite my answer on that having the most upvotes, the actual site policy seems to be "if it doesn't have an obvious answer, let's argue about whether or not it is answerable and have some close vote wars." Which is exactly what you occasionally see happen. The close votes usually are driven by either the "there is no answer, so this should be closed" argument1 or the "we don't know what the developer was thinking, so this is developer-intent" argument. Yes, most of the people making those arguments hate lore questions, but I think it's important to understand that they're (usually) not voting to close simply because the question is lore-related.
1 You might be saying "Woah, but that answer to that 'Should we close questions with no answer?' meta is overwhelmingly 'No, we shouldn't close them,'" but then you need to go check out this answer to a related meta, which is highly upvoted and written by a mod, which includes the point that we DO close such questions. This leads to a lot of ambiguity about how we actually handle them.