The title says it all, and I'm asking this because I've noticed that a surprising amount of races seem to lack lore, which is something I want to fix. I plan on writing lore for these races, such as Harengons, Gem Dragonborns, and a few others. Unfortunately, I'm new to D&D, and I don't know which races lack and have lore, so if you could please recommend me some, I'd be extremely grateful. Thank you!

Yeah, there's not much hard lore in most of the recent books, particularly the ones that are meant to be general resources like the PHB or Monsters of the Multiverse. This is the weakness inherent to D&D choosing to play to its strength as the iconic "build your own setting" TTRPG: they're trying to avoid giving canon/correct ways everything is supposed to be setting-wise. This unfortunately leaves newcomers who've just bought the new PHB rather short on roleplay prompts- the overall lack of which being my biggest complaint about the new PHB by a large margin, not just for races but for classes and backgrounds as well. Really, if you are looking for prompts and don't have someone sharing some of the older books that sadly are no longer on the market here like Volo's Guide to Monsters or Mordenkainen's Tome of Foes, the D&D wiki can give you a lot of exposition about the lore that's build up over the decades, although don't expect everyone in a group to be on the same page about it all- like I said this has been going for decades, so there's a lot of room for different experiences with the various pieces of the lore. If you want a more detailed talk on how the topic of racial/species lore can be handled, see below.

Some people in these forums have said that it's very necessary to push back against concepts like "racial essentialism" and "biological determinism" by not trying to define what exactly dwarves, elves, etc. are in terms of social structure, values, and such in any strong terms. I understand the concerns about reinforcing the specious arguments that have been put forward irl about how those concepts relate to various demographics, and to be fair some of the earlier 5e material wasn't in the best area still- the write-up on orcs in Volo's did still lean pretty heavy on the "excessively brutal and savage barbarian tribes" archetype. Although, to be fair, while the bit about "constantly watching for signs from their gods" can parallel unflattering representations of several real world cultures, given that the existence of gods who do communicate by various means with mortals is a rather significant facet of D&D, that actually holds up as an understandable attitude.

But anyways, while there have still been points that could have used more polish within the scope of this edition, at the end of the day in the context of a speculative fiction setting, embracing the Planet of Hats trope to some degree is a necessary expedience to present distinct and digestible cultures. These cultures don't necessarily need to break down along racial lines, of course, but again given that D&D has been moving away from having a default setting for a long time, it's rather hard to find another demarcation that might transition across setting lines or into homebrew at all. It still won't be perfect: as Elgate noted you'll find vey different lore about Orcs in the Forgotten Realms vs Eberron, although it's worth noting that Eberron was specifically written as a setting that drags the concept of the traditional morality and other expectations that had developed around points like orcs, the undead, and the various kinds of dragons into a dark alley and repeatedly clubs it over the head with a 2x4. You'd find a lot of parallels in presentation between elves, dwarves, etc. between say Krynn and the Forgotten Realms, although the radically different histories certainly meant there were pronounced differences in the characterizations as well.

Frankly, I think that- in a similar vein to what Elgate discussed- they could have used the hard features of the races in the new PHB as talking points to give a majority trend and a few differing ones. For example: "While the long lifespans of the elves instill in many an appreciation for careful deliberation, respect for tradition, and focus on honing a particular craft, art, or skill to perfection, others instead take the opportunity to continually seek out new experiences, try their hands at new challenges, and trust that their many years will allow them to quickly arrive at the solution for a problem. While an adventurer's life naturally provides many opportunities for fresh experiences for those elves actively seeking them, it can likewise draw in those whose enduring dedication to serving an ideal, pursuing knowledge, or honing their skills in the heat of battle has stood the test of centuries." Paints a nice vivid picture but also hopefully highlights various possibilities rather than putting elves into one particular box. Much more helpful for trying to flesh out a real character than anything you'll find in the '24 PHB.

Essentially, all races lack any sort of meaningful lore. Individual game worlds can be different, sometimes radically so - Eberron has super neat lore, but it's ranked third at best, behind the original Planescape and Dark Sun. Forgotten Realms also has ... admittedly deep lore, only it's all kinda meh. Or. Something. It's standardized, it's like oatmeal. It has everything a growing boy needs, unless he needs something other than elfy elfs, dwarfy dwarfs .. and so on. 

Sidenote: I really don't like harengons, but check out Usagi Yojimbo (it's a comic book) if you want what I think is the best possible take on them. Maybe that's even the inspiration for them? I dunno. Sorry if I'm pointing you to the most blitheringly obvious idea, thinking I'm contributing =D

So, are there races with large amounts of lore, and would going all out with defining things like what I plan to define (History of the race, traditions, pantheon, social hierarchy, government, grammatical analysis of language complete with letters, verb endings, and whatnot, etc.) be too jarring for D&D? While I want to make lore, I still want to make sure that it fits in.

Quote from TheFoxRunningThroughTheForest77 >>

So, are there races with large amounts of lore, and would going all out with defining things like what I plan to define (History of the race, traditions, pantheon, social hierarchy, government, grammatical analysis of language complete with letters, verb endings, and whatnot, etc.) be too jarring for D&D? While I want to make lore, I still want to make sure that it fits in.

 You can do whatever you want with the lore, but you should make sure your players know. 

Whenever I start a new game, I inform players that:

• I don't use other people's stuff
• I don't run premade adventures
• If you encounter something that sounds like you know it - like a goblin - you don't, it will be noticably different from what you read about in the Monster Manual
• And of course I inform them of lore their characters would know about at creation

And even with that out of the way, there's always someone who complains that 'dark elves can't do that' or 'I think you got the AC of this monster wrong'. So be prepared for pushback. People simply feel comfortable with the stuff they can look up. Even when you inform them that goblins live in fiercely competitive magocracies, they're still surprised to find that goblins aren't dirty, malnourished little critters that live in holes in the ground. Because even when you tell them it's different from the books - they look to the books. Some do, by no means all.

I should add: 

It's not about liking what I like. It's about the difficulty of communicating 'what is this game'. I make kinda niche games - and people still sign up, expecting them to be mainstream, despite my efforts to communicate that ... if you're expecting a straight Phandelver experience, you will be much disappointed here =)

Fair point, there’s a lot I didn’t consider here. Thanks for the help!

To be fair, the core Forgotten Realms setting- the area covered by the Sword Coast book- basically just has the one general/human pantheon that is actually only slightly larger than the pantheons for dwarves or elves going by Mordenkainen’s Tome of Foes. Granted, most others do fall well short of the same count, but it’s not like humans alone get an orchestra while everyone else just has a lead singer and a few backup dancers. There is clearly a bit of a slant to who got the most attention, but as a practical business exercise there’d inevitably be a point of diminishing returns and arguably from a worldbuilding perspective having an uneven distribution is more “natural” than having a standardized list every pantheon works off of.

Quote from Elgate >>

There has definitely been a step away from giving monolithic lore to species in D&D, such as saying things like 'Well all dwarves hate goblins'. The corebooks are also now tending towards letting setting books state their own lore, so that orcs in Forgotten Realms and orcs in Eberron can have very different lore, without either one being the 'default' lore.

Mostly because lore really would come down a lot more to history and region. Elves from the artic forests, in smaller more special (species) homogenous groups, far in the north of your setting really should have a different culture to the elves living thousands of miles off to the south, in a multispecies nation, with both groups having very different culture, shaped by their regional environment and historical events. 

But D&D is also more creationist. Outside of humans, most species tend to have a particular god or pantheon they all seem to credit for their creation. This does tend to lend towards a more unified culture when it comes to origin myths and faith, although even in D&D we've seen different nations of a species favour different gods or have disagreeing origin myths. 

It can be a fun thought experiment to think about how certain innate traits (such as longevity, the ability to fly, the ability to see in the dark, resistance to poison so on) could influence how a particular species might develop a lifestyle or culture. Take how Krynn Minotaurs used their very cool 'Labyrinth sense' (The ability to never get lost in a labrynth, know the directions innately or 'can perfectly recall any path it has traveled.') to be able to navigate the seas expertly. 

Maybe sea faring dwarves could use their stonecunning ability to be able to navigate reefs more easily, and could use their poison resistance to consume foods (Like fugu!) that other species might struggle with. Maybe a multispecies city really never does sleep, as it's nocturnal species, such as those adapted to the underdark or who have dark vision, can work and be active at night.  Maybe like how humans get depressed with a lack of sun, underdark species can get sun stressed and suffer mental health effects with too much exposure to sun (Hello old sunlight sensitivity). Species with flight may build homes far above ground, or with no doors at the base for safety. Maybe longevity means that tracking all of your living relatives is even more important or actually less important, because Great-great-great-great-grandma is still alive and you have 150 cousins of various orders removed. Maybe longevity means cultural change is slower as you still have multiple older generations who remember older traditions.

And naturally, like with humans, having a shared culture or history is no guarantee that everyone in that group is going to think or act the same. 

 Just a note to say this was an excellent and thoughtful post.