Rather unimportant, but also immensely interesting fluff wise. Would it be feasible for any regional differences between temple cities' usage of Saurian? I would say fairly likely if it calls for any temple city to deviate from standard procedure in order to decipher plaques and other mysterious stuff. Another good case for idea drawing are some of the cultural differences too - Tlaxtlan primarily focusing on astrology, Hexoatl's militaristic status, and so on.
Lizardmen are very conservative and have a fairly stagnant society. This would suggest very little development of dialects.
Lizardmen temple cities are very old and mostly isolated from each other and the world for centuries at a time. This would suggest very strong dialects developing.
I guess it's up to fluff writers to figure out which of these is stronger.
In my own fluff I've put forth the idea that Lizardmen in Lustria and the Southland and really different accents. Now accents in foreign language are very hard to translate. I made Southland's Lizardmen sound like ye olde English with "thees and thous" and a sort of snooty context, but that's probably not a good metaphor.
I do figure that since Lustria and the Southland were separated for thousands of years and the Southlands has generally much less contact with warmbloods that they would develop distinct dialects. The Southlands also has fewer Lizardmen in it, and only one major city rather than four. I'm guessing the Southland's dialect of Saurian is a lot closer to the original dialect of Saurian spoken beofre the polar warp gates broke than the Lustrian's dialect.
Going over the Big Four.
Hexoatl's Lizardmen are on average, more active and dynamic than the Lizardmen of elsewhere, so they'd probably have more linguistic idioms evolving. They are the most militaristic city so they militaristic jargon and cadence probably permeates the language in peace time not unlike a military base or training camp.
Xlanhuapec is probably the opposite. They rely on stealth and misdirection to protect themselves so they probably have the least contact with outsiders of the Big Four. They are likely the least proactive of Lizardmen so they probably have relatively little linguistic evolution. Because of their comparatively low population, a love of being subtle, and a culture of being mysterious, they are probably terse when they talk.
Itza is the biggest city and they are the centralized city. It's likely they are the city that is most likely to meddle with other cities so they are probably going to have a lot of influences from other temple cities and kahoun influence their linguistic idioms. They are likely to be conservative and resist change though so they probably dislike slang and like formal speak.
Tlaxtlan Lizardmen would have the stereotype of having their heads in the clouds, almost literally. I'm betting even the Skinks who are not priests are more contemplative and methodical. They probably speak slow and carefully. Given that their leaders have to debate nuances of prophecy and lore they probably have a culture of not giving a straight answer and playing devil's advocate.
Lizardmen in Kahoun and occupied ruins might be the salt of the earth type. They have far fewer Slann and more contact with the jungle. They have smaller populations and lots of work to do so they are probably very pragmatic. They are probably the Lizardmen equivalent of country bumpkins. I don't know what this would sound like in Saurian. Given that they are often literally down in the mud, they probably use cruder slang.
PS I indexed this under
Day to Day Culture