Although beings with a mix of humanoid and reptilian features do exist in some mythologies, none have much resemblance to lizardfolk as they exist in D&D, and it seems plausible that Gygax had something like Howard's race in mind when he created them. (Having said which, reptilian humanoids did also exist in SF at the time; Doctor Who's Silurians pre-date D&D, for example, but seem an implausible inspiration).
The race is described as semi-aquatic, breathing air, but apparently able to hold their breath for a long time. They have a remarkably tough hide - as effective as chain armour - and, with two hit dice, are comparable with a gnoll, the strongest of the 'tribal' humanoid races. They are notably slow moving on land, presumably shambling along in a B-movie monster style, but are much more graceful underwater.
Most have a decidedly subhuman intelligence, and seem to use little in the way of tools or weapons, other than their sharp teeth and claws. A relatively rare version with more human-like intelligence also exists, and, judging from the picture, wears loincloths and simple adornments, as well as using shields (spiked clubs, are, however, the standard weapon - the one in the picture has presumably stolen its sword from a victim).
Communities average around two dozen individuals, and are, given their usual intelligence, probably more accurately described as 'packs'. They lair in caves on the edge of swamps, and, while they can eat vegetable matter, prefer flesh, and, for some reason, human flesh in particular. While they do have their own language, the impression is of bestial man-eating monsters lacking even the culture of orcs.
The 2E version has legs that are no longer humanoid in shape; they have the long toes found in many lizard species, but an ankle that's raised high off the ground, which is a more mammalian arrangement. (Of course, real-world lizards aren't normally bipedal, either). This ought to imply speed and agility, although, in fact, they're as slow as ever.
Although typical lizardmen are no more intelligent than before, and still lack a material culture, they seem far more organised than the 1E version. Communities can number over a hundred individuals, sometimes cooperate with neighbouring bands, and have a hierarchy of leaders based on combat prowess, and even a few spell-casters. This time, therefore, their description as 'tribal' seems more justified.
It's in 3E that the name of the race switches to the gender neutral "lizardfolk". The tail looks heavier now, and has a more crocodilian appearance, while the snout is much shorter than before. Most notably, there is a large, brightly coloured crest on the back of the head, although, otherwise, the usual greenish-brown mottled colouring remains. The teeth are much less effective as weapons than before, and they normally avoid biting in combat.
The truly bestial nature of the original lizardfolk fades with this edition. No longer are they slow and shambling on land, now moving just as swiftly as humans do, and their intelligence score has increased by a full 3 points, although that's still lower than the human average (they've overtaken orcs, though). All of them now seem to use weapons, and presumably other tools, although they're admittedly crude.
The only significant change to their society since 2E is that it's now apparently patriarchal, which is ironic, considering the way that the name of the race has changed. It's also odd, considering that females are as physically strong as males, and, since they lay eggs, aren't inconvenienced by pregnancy.
We're also specifically told that lizardfolk don't really prefer to eat human flesh, as they did before, although they aren't opposed to the idea. They no longer have their own language, now speaking the language of dragons.
The 5E version has lost the mottled pattern in favour of a blander, but more verdant green (of course, there may be more variation between individuals than we can see from a single image). The legs are actually more lizard-like than in the 2E and 3E versions, but without the almost fully-human appearance of 1E. The crest on the head is even more flamboyant this time, and doesn't seem to be supported by spines - presumably, it's made of some particularly stiff skin. In 3E, they could comfortably hold their breath underwater for about five minutes (it's not specified in earlier versions), but now it's up to a full fifteen.
In other changes, they can no longer fight with their claws, their teeth are deadly once again, and the intelligence has dropped back down to just a point above the 1E version; they retain the full speed and the ability to make their own tools and weapons. Culturally, they are similar to the 3E version, although there's a specific explanation given as to why their strongest leaders are all evil, when the race as a whole isn't. They do, however, all live in huts now, even if the huts are sometimes inside caves.
Given that they live in swamplands beyond the fringes of civilisation, and that they are usually portrayed as isolationist, it's unsurprising that lizardfolk receive little mention in most game world descriptions, beyond perhaps a list of wetlands where they may be found. In Eberron, they have quite a sizeable homeland on the eastern coast of the main continent, while in Golarion, they are apparently widespread across the vast southern jungles, but both versions seem to fit the standard model.
Those in the Forgotten Realms apparently have darkvision, despite being one of the relatively few races in the core rulebooks that don't. According to a sourcebook written for 2E, they also need to keep their skin moist, which is a really weird thing for a reptile to have to do. In fact, reptilian humanoids in non-D&D game settings, such as Yrth, are often desert-dwelling creatures. Another common trope is to have them herd, or even ride, dinosaurs; this is seen in Warhammer and Glorantha, for example.
BiologyWith that covered, let's consider how lizardfolk would work biologically, if they really existed. In many respects, reptiles aren't all that different from mammals anatomically, and, in this case, that is further enhanced by the necessity for a bipedal, mostly humanoid, anatomy. Nonetheless, of course, there are some key differences.
A significant one is that reptiles are "cold-blooded", which is to say that they do not generate a significant amount of internal body heat, and have to warm themselves up by basking in the sun, or using some other external source. This fits with the idea that lizardfolk live primarily in the tropics, although it does imply that they would be more sluggish at night, or in the cold environs of a subterranean dungeon.
A key trait of the D&D version of lizardfolk is that they are semi-aquatic, something that is unusual in real-world lizards. (It's less odd in other kinds of reptile, including turtles, crocodiles, and sea snakes, but we'll assume, where possible, that lizards are going to be the closest analogue). But that's not to say it's unheard of, with marine iguanas being, perhaps, the most dramatic real-world example. Marine iguanas do have a problem with water typically being cold, and need to bask a lot after taking a dip in order to restore their ability to move rapidly, but the fact is that they can stay underwater for up to an hour, which actually beats any of the quoted figures for lizardfolk. So it's unlikely to be a problem, physiologically.
Lizardsfolk are also, as one would expect, scaly, and lack the fur of mammals. If they are truly like lizards, they need to periodically shed their skin as they grow. Unlike snakes, however, lizards do not shed all their skin in one single piece, and instead drop little bits here and there, so it isn't quite so dramatic.
Lizards also have a sensory organ in the roof of their mouths that allows them to "taste" the air, by flicking their long tongue out, and then bringing it back inside to present any wafted molecules it may have found. Referred to as Jacobsen's organ, this is actually present in most mammals, too (although used in a slightly different way), even if it's lost in higher primates such as ourselves. Most descriptions of lizardfolk don't indicate that they have exceptionally keen senses of smell however, and the organ is often reduced in aquatic animals, so it may be that this has little practical effect in their case.
Some lizards also have a "third eye" on the top of their heads. But it's entirely covered in skin (and hence, pretty much invisible), extremely small, and can only detect the difference between light and dark. If lizardfolk even do have this organ, it's hard to see how it would have much practical effect.
Since real-world lizards are quite variable (think iguanas, geckos, skinks, and chameleons, for example), it's hard to make other generalisations. For instance, while the great majority of real-world lizard species are carnivorous, the marine iguana is one of the exceptions, tending to eat seaweed. So it's hard to say that lizardfolk have much in the way of a direct equivalent that we can point to.
One thing we do know, though, is that lizardfolk lay eggs. This is worth noting, because a surprisingly large number of real-world lizards don't - including the semi-aquatic Chinese crocodile lizard. So live birth would not, in fact, have been implausible, had it been present. The size of lizard eggs in proportion to that of the mother varies considerably, but, if we guesstimate a similar proportion to that in the marine iguana, we're looking at something about 22 cm (9 inches) long, and weighing at least 1.5 kg (3.3 lbs).
In most lizards, the eggs have a leathery, rather than calcified, shell, and they would have to be kept in a dry nest of some kind. They probably take several months to hatch (the world's largest living lizard, the Komodo dragon, has an incubation period of around eight months).
On the subject of reproduction, lizards, unlike mammals, and, for that matter, crocodiles or turtles, have two "penises". These are kept invisibly tucked inside the body when not in use, which renders the loincloth of some illustrations a bit pointless, and confirms that it would, indeed, be hard to tell the sexes apart without a thorough physical examination. (Lizardfolk themselves can presumably tell, perhaps because they give off different pheromones). Besides, they only use one at a time, so that's all right.
Since there is some variation in the specifics, converting a D&D lizardman to other systems may depend partly on the specific kind that is being converted. Once that is decided, though, as with most low-level humanoids, any conversion is likely to be very straightforward.
Generally, they are stronger than humans, but not by all that much, and they have a tough physical resilience that may, in some systems, be partly related to their marginally larger-than-human size. They have a low, perhaps even bestial, intelligence, and may, or may not, have claws and/or teeth sharp enough to be useful in combat.
Their two key special attributes are the ability to hold their breath for long periods of time and a hide that's equivalent to medium armour. Their combat ability is likely that of a competent, but not remarkably skilled, warrior.