Lizardfolk has me completely stumped RP wise. I really like the idea of a Lizardfolk - Cleric of the forge from Xanathar's. The thing is... this race just doesn't care about anything except survival... They don't want or desire anything from what I understand.
Do these creatures have religion? Since they have no moral system or want/need for anything greater than living, would it even be possible to explain how one would be a cleric?
Also, how would I RP them? Do they speak in first or third person? How do they interact with others?
Personally, this is one of the issues that I have with the way D&D has assigned a pantheon of gods to nearly every race.
I put lizardfolk in a category with troglodytes, bullywugs as having a more primitive form of religion, if at all. They would have something more like a shaman than a cleric, and perhaps closer to our understanding (or lack thereof) of primitive man.
So their religion would be one of ritual significance. Do they gain the strength of their fallen heroes by eating them, burying them, or something else? Another question to be answered for both ritual and practical purposes is the use of fire. Do they use it? If not, are they afraid of it? What about natural events in the world? Their religion could be more like a series of superstitions centered around food, life, reproduction, and death.
The problem with all this, is that it doesn't work well for PCs (one of the reasons why I don't utilize most of these types of races as an option for PCs). Having said that, if there's a lizardfolk that rises above the normal aspects of lizardfolk life and is gifted with greater intelligence and wisdom, they might question their existence in ways that others don't. And this is a world where the gods to provide direct evidence of their existence in the granting of powers to their faithful. Obviously a druid or cleric of a nature god makes sense, with probably a god of war as another possibility.
In terms of how they speak? Again, I question the usual approach that every creature can speak common. In my campaign, their language would be one that could be spoken and understood by other lizardfolk. Most likely they wouldn't be able to replicate our language, and we couldn't replicate theirs. Communication would be awkward, and make things interesting. Of course, most groups probably wouldn't want to go to such troubles.
I find it interesting to really think through their society as a whole. I love lizardfolk (and I'll have to make it clear that mine bear no relation to the stuff in Volo's Guide). In my campaign they are capable of both bipedal and quadrupedal movement, and can climb and/or swim. They are sort of a cross between small lizards and crocs. They are loosely tribal in nature, with a lizard man "king" ruling over a region through strength and force. They've learned to band together most likely as a defense against other monstrous races such as goblins and such.
There are quite a few variations, trogs being one. Due to them all being carnivores, they are semi-nomadic in their homelands, with some exceptions where they can imprison and raise livestock. Other races (intelligent or otherwise) are judged for their usefulness as food, and whether they pose a threat or not. They haven't developed mining, metalworking, or a money-based economy. They tend not to have valuables beyond what they can carry, and weapons are centered around weakening their prey through ambush (spears or slings, bows are not common, especially among the swamp-living varieties). The swamp varieties will ambush and attempt to drag their prey underwater and grapple them until they drown. Non-swamp types might use (or have natural) poisons on their spears and arrows (if they use them). Armor needs to be very flexible and not provide a disadvantage in water, or be too hot in hotter climates. They are cold blooded, and have activity cycles (another reason they have banded together in loose tribes). I tend not to allow wizards, just sorcerers or warlocks. Probably no paladins either. That doesn't mean there can't ever be an exception.
From there you can extrapolate what might occur if one was more intelligent or wise than the others. It will depend on your campaign - are you part of a tribe, or a lizardfolk in human society? Also, in the realms one of the creator races of ancient times is an ancestor of lizardfolk and other reptilian races (except perhaps yuan-ti). So they could be seen as a degenerative race that has regressed from their former glory (in the Realms that was 30,000+ years ago).
A more "advanced" race may be part of a human or humanoid barbarian tribe. A clan that was once on their own, but as territory and prey has been reduced they banded together. And the more advanced of those could find themselves within the greater human civilization.
I do have much more advanced tribes in far away places, like the jungles of Chult, and the Shaar, where humans and elves don't dominate. I guess the bottom line is, take what Volo's has, work with your DM and figure out where they fit into the setting as a whole, and then build from there.