Even more Lesser-known anime you might like or at least want to check out.

The Swiss Family Robinson

Everybody has heard of the book The Swiss Family Robinson. Not nearly as many as have actually read it. It's had quite a few TV and movie adaptations over the years though, especially through the 70s and 80s. Japan gave us arguably one of the best (if not particularly faithful) adaptations with "The Swiss Family Robinson: Flone of the Mysterious Island". It's a lot better than you'd expect from an early 80s anime and I've read it was pretty popular in Europe for a while. While it did get an American release, I've met very few people in the U.S. who even know it exists. (You can watch it on Amazon Prime video, fyi.)

Planetes

If there's one thing anime doesn't do very often, it's hard sci-fi (a.k.a. science fiction with a solid base in real-life, modern day science). Planetes is here to show that anime can not only do it but do it well. Instead of giant robots or improbable aliens, Planetes is all about garbage men in space. Really. Turns out that "space junk" is a real problem that exists in the modern world that we'll have to start taking care of soon if we want to keep exploring the solar system. (https://en.wikipedia.org/wiki/Space_debris) Planetes gives us the story of some of the people who go out and risk their lives to pick up that debris and keep ships safe.
It might not sound exciting, but it's got lots of colorful characters, space terrorists, and a group of unemployed moon ninjas.
Also, this show has probably the greatest tagline ever: "In space, a bolt can screw you."

Murder Princess

This one is a pretty short series, almost an OVA at just six episodes long. But that just means that it's a quick impulse watch you can crank out in an afternoon. It's a fun, action-packed show where a princess on the run accidentally switches bodies with an infamous bounty hunter. The bounty hunter decides to take the princess' place and help her retake her kingdom by killing every last bad guy she comes across. As the cliche goes: her business is killing and business is good.
There's also a kinda/sorta, "will they, won't they," maybe lesbian subplot about the princess and bounty hunter wondering if they're in love with each other or if they're really just narcissists in love with their own bodies.

Third: The Girl With the Blue Eye

Third is a really difficult anime to explain. It's got a somewhat complicated premise, but if you can get past that, it's quite enjoyable.
So, after a really bad world war, mutants (who are basically techno-elves with a third, red eye in their foreheads) rule the world from a space station and tell the normies that they can't have technology past a certain level since it was the cause of the last war. So then this girl Honoka is born and she's a mutant with a blue eye instead of a red one and doesn't look much like an elf. The Third eventually decide she's not one of them and send her back to Earth, which is mostly a Mad-Max-esque desert planet. So as a teenager she takes her chi-powered katana and super powerful tank and becomes a mercenary/gofer for anyone willing to pay her. Also she has a few sidekicks like the AI that controls her tank, a love interest with a "mysterious past" (i.e. you can totally tell he's really an alien in human form from when you first meet him, why are they trying to make it mysterious when it's so obvious?), and a well-endowed lesbian who is far more interested in underage Honoka than she should be.
It's not the most original or trope-free anime ever but neither is it plagued with a lot of the regular cliches, so it's probably worth your time.

Moribito

Okay, this is a series where I have no idea how it hasn't become more popular. It's just incredible. Great animation, amazing action scenes, and an intriguing story that has almost none of the normal anime tropes. Balsa is a hired bodyguard who cannot rest until she saves the lives of eight people to atone for eight lives that were taken protecting her. She has one left to go when she is hired by a queen to take her son into hiding for an indefinite period of time since his father wants to kill him. But it turns out there's a lot more going on than meets the eye of any mortal.
Now, the only reason I can think that Moribito hasn't done better is because it's different from just about every other anime series I've ever seen. It starts out pretty fast but it slows down somewhat as it goes on. But I'm telling you, it doesn't get any less interesting. If you're tired of all the same anime tropes and characters or just want something that isn't a "normal" anime, you just might like Moribito.

009-1

Part James Bond, part Cate Archer, part retro-futurisic; 009-1 is a sci-fi spy anime that takes place in an alternate future world where the cold war never ended and the East and West use super-spy cyborgs against each other while mercenary spy groups wait in the wings with their own agendas. Expect lots of cloak-and-dagger, a decent amount of action, and more than a little gore.
While talking to the few people I know who've seen this show that the older style of art 009-1 uses often gives the impression that this is a kid-friendly show. THIS COULD NOT BE FURTHER FROM THE TRUTH!!!!!!! Sex, nudity, and graphic violence abound. Heck, they even manage to combine it sometimes. For example: As a cyborg, Mylene (the main protagonist) has breasts are also machine guns. (I'm a little scared at how many "that's my fetish" gifs might show up in the comments when people read that.) This show is great, but it is certainly for adult audiences only.

Gunslinger Girl

I really don't have enough superlatives to describe this show. It's got little girls turned into cyborg super assassins, realistic gun porn, and some pretty heavy philosophical questions that aren't rammed down your throat. All this while putting it in a context that makes you really care about happens to the main characters even as you watch them perform morally ambiguous actions that make you question if they're the good guys or the bad guys.
It has a sequel series that I've never seen but keep meaning to. Anyone able to tell me if it's worth my time?

Ergo Proxy

Okay, this one probably doesn't qualify as "lesser-known" but I'm putting it in this list since I'm qualifying it as "not well-known enough." This is near the top of my favorite animes ever. Not necessarily because of the story (though it is really good, if also very Geneon) but because it's easily got the most beautiful art direction I've ever seen in any cartoon series. It equals or surpasses most movies, and it manages to keep it going for a full season. Seriously, it's just gorgeous. If you haven't seen it, you owe it to yourself to go out and watch it for the visuals alone.

Claymore

All right... I admit this is another show that almost certainly doesn't count as "lesser-known." But while most people I know have at least heard of Claymore, a surprising amount of people I've talked to haven't actually watched it.
Claymore is about a fantasy world where a mysterious organization is trying to save the world from human-eating demons by surgically altering little girls with demon flesh and turning them into "claymores" so they have the power to kill said demons. Unfortunately it also has the unfortunate side effect of sometimes turning these claymores into human-eating super-demons. Needless to say, their life expectancies aren't very high. Yeah, it's a pretty depressing world.
If I'm going to be completely honest, Claymore isn't a whole lot more than a shonen anime with graphic violence and girls as the protagonists instead of guys. But it really is one of the best shonen anime I've ever seen. By which I mean it's one of the few shonen anime I've seen that I actually like. And I like it a lot. It's biggest problem is that there was never a second season, even though the manga apparently goes on for quite a while after the point where the series ends.

Hey, thanks for making it all the way down. If you want to check out some more (mostly) lesser-known series, check out my previous lists:
Lesser-known anime: https://imgur.com/gallery/PDcCS
More lesser-known anime: https://imgur.com/gallery/Rdn3h