I'm actually playing a Lizardfolk Monk now...
And I played a Lizardman back in 2e. For me, the way I approach the character is by thinking about brain structure. Since Lizards don't have Paleomammalian Brains (and yes, I know the Triune Brain Hypothesis may not mean squat, but it's useful for my purposes) I assume that my Lizardmen *don't have emotions as mammals do*. Basically, all that matters to my Lizardman is getting enough food, propagating the species, and either destroying any threats or avoiding those threats he can't destroy. He's pragmatic, intelligent (he has a 14 Int) and utterly willing to sacrifice anyone in the party to preserve his own life without being especially sinister or malevolent. In essence, he's amoral; he won't waste effort to do something just because it's the 'evil' or 'good' thing to do, but convince him it will allow him to accumulate enough power to ensure his own survival in the hostile human culture he finds himself in and he'll jump for it. Kind of enlightened self-interest. It's not too hard to comprehend as a human, and yet it's reasonably alien from the way we think.
I'm actually working on a campaign set 65 Million years ago on Earth, based loosely on Lovecraft and REH, with various reptilian races from the Monster Manual and Dragon as PC races. At present, I have Lizardfolk, Kobolds and Troglodytes as well as Sean Reynold's Saurials, although in all cases I don't use those names. I may use Yuan-Ti abominations as the 'Drow' of the campaign, along with Loacanth and Kuo-Toa as rivals and Illithids as the great evil race of the campaign, in service to Undead Trilobite-Gods (Think Aboleths and Alhoons) that want to destroy the reptile empires by bringing the long-imprisoned Tarrasque down from its prison in space. The great thing is that the continents were so different back then that it's possible to use actual maps of the earth and they're barely recognizeable. I think homebrews are more fun that way: you can do anything you want with them. It's interesting to consider what a reptile society (well, reptile/saurian, anyway) would be like. How do they interact? How does such a group decide on a political structure?
This doesn't mean I don't like elves, dwarves, et al: I do, actually. I just like playing around with other options sometimes.