Volo's Guide to Monsters talks about how to do it, I believe.
If you wanna stay true to vanilla, the lizardfolk character will lack a lot of "monkey brain" qualities such as
pride. They won't do stuff like boasting about or downplaying their qualities. This means they may be very
physically territorial about certain things such as their belongings, but are never vindictive and petty about it.
I suggest reading up on some
laconic phrases. The Spartans are a good source of inspiration for that, and laconic humor is a great way of having your character not be a stick in the mud, and it's likely to be unique to your character specifically in the party, making them much more memorable with not too much effort.
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