To me it feels like recent publications have "roboticised" Lizardmen, particularly Saurus. I don't know whether it's just me picking up on it more because I'm older now, or that it has actually changed over the years but it just seems to be the case.
I for one think that giving your characters a bit more depth and, dare I say it, "humanity" allows you to empathise more with your chosen army. It's why even though Tyranids (40k) were my first army I found it hard to think of them as my army, any why I felt Necrons (again, 40k. It's in my blood sorry!) were boring at the time of their release in 3rd edition 40k. Your General is supposed to represent you on the battlefield - by making him/her/it too alien for you to relate to it really detracts from the immersion of the hobby and really makes it nothing more than a game (which is 100% OK if that's what you like about Warhammer).
With Lizardmen you can get around this in a few ways without breaking the fluff depending on who your "characters" are, who you see yourself as and who you want to interact with who.
Skinks are easy. They're the most human of all the Lizardmen species. They're nimble minded, independent and capable of quickly learning new roles within Lizardmen society depending on the current need. They're warriors, artisans, scholars, priests, labourers, hunters, messengers, clerks, accountants, herdsmen, traders. Almost any human occupation can be paralleled by skinks. The only thing to keep in mind with Skink characters is that unlike humans they will never be entirely self serving. Yes they might be greedy, selfish or cowardly but ultimately their loyalty lies with their City, the Slann and the Old Ones and that loyalty is unflinching.
Saurus are a mixed bag. I like to think of them like domestic dogs. There are hundreds of different subspecies of Saurus that were selectively spawned for specific traits (like a dog breeder will breed/crossbreed certain species or individuals to obtain certain physical traits or temperaments). Some are spawned for cold emotionless robotic killing, some are spawned for unflinching loyalty, some for bloodthirsty ferocity. Some because they have harder skin, sharper teeth, certain colours, longer tails. Some are placid and slow to rouse without orders, some twitchy and quick to kill. The possibilities are pretty broad as long as you remember at their core they are sill Saurus Warriors - selectively bred as obedient soldiers in a genocidal campaign against everything their creators perceived as wrong. Some will be dumb dumbs that only know how to say "Hulk smash", some will be very keen minded with an immaculate attention to detail but might have very poor communication faculties outside of body language. Some might be super smart and understand everything that's going on around them, but due to their preconditioned purpose it just might not occur to them to tell anyone what they know.
Kroxigor are also pretty easy. They're the most robotic and mindless subspecies, but that doesn't make them uninteresting clones. Think of them of an extreme case of the domestic dog analogy above - they're bred to be big and strong and loyal and all that annoying intelligence has been bred out of them. They're big and oafish, but they still form bonds of companionship with their fellow Lizardmen - especially Skinks (who would directly interact and communicate with them much more than Saurus would). They are the big friendly guard dog that knows the family and wouldn't hurt a fly.... unless that fly strayed onto his territory or his owner says "kill".