Just so we're all on the same page: it's weird that Lando was humping up that robot, right?
A "self-made droid" built from astromech and protocol parts,
L3-37 is an enlightened navigator who cares deeply about droid rights.
L3-37 has a lot of problems as a character (beginning with the fact that they just frigging named a droid "leet" and left it at that), but a lot of them seem to stem from the way Solo was made: it was originally meant to be a screwball comedy, before being turned serious by Ron Howard; consequently, there are some things that feel like holdovers from those earlier drafts; things that, in context, were meant to be jokes, but have been presented here straight. Consider the scene where Han is given the name "Solo" by some aiport information kiosk worker: imagine that showing up in The Lego Movie or Robot Chicken, and it could definitely get a laugh; play it straight, and it's just an awkward, mockable moment. The same kind of thing seems to have happened with L3-37's whole deal, which would explain why it's impossible to tell whether the character and her desires are supposed to be taken seriously or if she's a punchline.
L3 was voiced and mocapped by Phoebe Waller-Bridge,
who managed to sound 100% like Captain Phasma. The pitch of her voice, the modulation, the accent... admit it, when you first heard the droid speak, you thought it was Gwendoline Christie again. The toy needs better paint apps for the eyes - they look unfinished. And why is there an Abstergo Industries logo on top of her head? I thought she was a navigation droid, not an assassin bot!
In-universe, L3-37 began life as an astromech droid - an origin you can still spot hints of, since her upper arms look
like R2-D2's legs. Her original owner forgot to replace her restraining bolt, so she took the opportunity to build herself a new body and upgrade her memory capacity. She's obviously a female-coded droid, with a larger chest and distinctly round hips - the early plan was that she'd look like she was made from the same parts as the interior of the Millennium Falcon, but the final design is more about random parts than things that are identifiable.
Suiting her cobbled-together nature, L3 is skinnier and more "hollow" than droids like C-3PO - she's got the kind of gaps we could only imagine for him, because putting a skinny man in a costume was the pinacle of 1970s special effects technology, while today we have the ability to just remove actors' bodies when need be. Loose wires dangle past her joints, which might make you wary of moving them very much: she moves at the head, neck, shoulders, biceps, elbows, wrists, chest, hips, knees, and ankles. Her feet are barely more than flat pads near the ends of her legs, which is not great for stability. She has no accessories, because she doesn't use anything, but you know what would have been good? Let the toy pull apart at the waist for "battle damage" action.
L3-37's "droid rights" shtick might have worked better if Solo had remained a comedy: at least then it could have seemed like a running joke, and not just something all the serious characters rolled their eyes at and ignored? L3 was a character with potential, but she didn't really get time to live up to it. Her toy's well made though, and you can write your own adventures for her.