I would argue that you can't really have a roguelike without random level generation. Would you consider a game like DROD RPG to be a roguelike? I get the impression (haven't actually tried the game yet) that the game has a turn structure like a roguelike (you move, then the rest of the world moves), but the game is explicitly described as having no randomness, and there's even an Undo button (something that you would be unlikely to ever find in a true roguelike). So, is DROD RPG a roguelike?
I've never played DROD RPG (I've only played DROD), but while calling DROD a roguelike would be a severe stretch, I would probably say from the description that yes, DROD RPG is a roguelike. Even DROD is more roguelike than Sundered, or FTL, which is also called a "roguelike" (it even shows up in gentoo under games-roguelike <sigh>).
Games with fixed maps that are definitely roguelikes include Omega, tome (middle earth and a little maj eyal), Ivan, and some versions of Larn. Admittedly, all of those have some random maps (or randomness in their maps, such as population and ordering). The thieves' guild of Rampart, for example, may be in a different house every time, but the city still looks the same. These fixed maps were much bigger parts of their respective games than the town map of Moria, for example.
I'm sure many think permadeath is necessary as well, and, indeed, I can think of few roguelike games that don't do it. Nonetheless, back in the day, it was the one feature most avid players I knew ignored (by copying save games as needed), and therefore I don't think it's necessary. It's also a terrible feature for a game: Kobolds are uninteresting creatures, and making me fight them more often than anything else is just boring. Some people like that kind of thing, though. Personally I think it's little more than a way to justify the scoreboard, which is in virtually every roguelike as well, but not really useful in a single-player environment.
So, I guess I take back "neither necessary nor sufficient" and just say "not even remotely sufficient". If you want "roguelite" to mean "permadeath and random maps", that's fine I guess, even though I'll still cringe every time I see it, since the word itself is not properly defined anywhere (roguelike was defined at one time by comp.games.roguelike, but I don't know if they kept it consistent or if it's still around).
This reminds me of a concern I have had with another term: RPG. That term used to mean something when it comes to games, but nowadays people have been using that term for action games that just happen to borrow heavily from the RPG genre, without taking its core feature (namely, turn-based combat).
I would argue that it's statistics-based abilities, rather than turn-based combat. Or, to put it another way, the ability to do something should rely on the *character* rather than the *player*. Most of the time, this translates into requiring turn-based combat, but pause-and-queue systems with reasonable character AI seem just as correct. I make the same argument at tabletop games where the DM expects *me* to actually haggle, when it's *my character* who has the high charisma and/or bartering skill (but nobody expects me to actually cast a spell or be able to hit someone with a weapon, go figure).