Despite being a game 2 race, the Lizardmen need almost as much work as some game 1 races to be interesting. As they stand now, their campaign is incredibly boring and one-dimensional. Even with the introduction of Tehenhauin and Red-Crested Skinks, you are still almost always incentivized to go for Saurus and dinosaur spam. They are unloreful and missing things that make them unique (not just units). There are several areas where the Lizardmen need work.
Geomantic Web: This has a couple of different problems. (1) It's boring and pretty inconsequential in its current form; all it does is buff commandments based on its level. (2) It takes up a valuable building slot for not a lot of effect.
-To address the first problem, I would give it some kind of an active effect that the player interact with. According to lore, Slann can use the Web to communicate and send their magic from vast distances. So, I would change the Web so that any Slann you have access to can send their spells to the battlefield, even when they're not present (perhaps at a degraded effect unless the Web is at full power).
-The second problem is much easier to fix: either remove the Geomantic Pylon as a building or make it do something more useful than just giving an income bonus and making the Web stronger.
Primal Instincts: This is by far my biggest problem with the Lizardmen. Lizardmen are not primal and they are not prone to rampage. CA made a step in the right direction with the release of the Prophet and Warlock DLC, but it was only a bandage for a greater problem. Primal Instincts needs to be outright removed from the game and replaced with the actual trait that Lizardmen had in 8th edition: Predatory Fighter.
Instead of getting a buff and losing control when they lose a certain amount of health, Saurus and other Predatory Fighter units are supposed to (a) fight better when they are winning, and (b) pursue their routing opponent unless a skink character is nearby. This can be implemented by making Predatory Fighter units (Saurus and Kroxigors) get a bonus to melee attack when they are winning their current fight (similar to the Nasty Skulkers' "Opportunist Murderer") and forcibly pursuing their prey when their opponent routs. The downside (chasing the routing enemy) is negated by giving all skink characters an aoe passive which prevents units from chasing the enemy down. This change is loreful, follows the spirit and rules of the tabletop, and keeps the player in control of his units (instead of leaving it up to the opponent to decide when to force a rampage). A change from Primal Instincts would also coincide very well with the potential future introduction of the much-anticipated Troglodon.
Poison: Lizardmen have a lot of access to poison, but they are frequently also hit by their own poison attacks, making it fairly pointless. At a minimum, Red Crested Skinks are supposed to be immune to all but the most potent poisons (like Clan Pestilens' Censor Bearers). One of the things that differentiates Red Crests from regular skinks is their extreme resistance to disease and poison.
There is also the issue of only one Red Crested Skink unit in the game (when most of Tehenhauin's army should be Red Crests). I can understanding not wanting to bloat the roster with many kinds of skinks, but at least Tehenhauin should have been given all Red-Crested Skinks instead of Red-Crested with great weapons and regular Skink Cohorts. His buffs for skinks should also have been more akin to Skarsnik's buffs for goblins.
Slann: The most powerful mages in the world, one of the worst lord units in the game. CA is already aware of the Slann problem and has said they will address it. At the very least, Slann should be given access to all 8 classical lores and High magic, and ideally have the ability to have 2 lores (like Mannfred).