If I create a Lizardfolk Barbarian is AC calculated 13 + DEX mod + CON mod because Lizardfolk start with natural armor 13 instead of 10 like other races?
You can only use a single AC calculation at a time, you can't add them together. Here are a few examples of AC calculations:
Base AC (10 + DEX mod)
Unarmored Defense (10 + DEX mod + CON mod)
Natural Armor (13 + DEX mod)
Full plate (18)
If Unarmored Defense said something along the lines of, "While you are not wearing any armor, you gain a bonus to your Armor Class equal to your Constitution modifier," then you would be able to use that along with your Natural Armor, because AC bonuses stack with AC calculations. But because they're two separate AC calculations, you can only pick one.
In other words, "Your Armor Class equals X" means it's an AC calculation, while "You gain a bonus to your armor class equal to X" means it's an AC bonus.
If I create a Lizardfolk Barbarian is AC calculated 13 + DEX mod + CON mod because Lizardfolk start with natural armor 13 instead of 10 like other races?
AX calculations don't stack.
It will either be 13+DEX or 10+DEX+CON. Whichever is highest.
You can only use a single AC calculation at a time, you can't add them together. Here are a few examples of AC calculations:
If Unarmored Defense said something along the lines of, "While you are not wearing any armor, you gain a bonus to your Armor Class equal to your Constitution modifier," then you would be able to use that along with your Natural Armor, because AC bonuses stack with AC calculations. But because they're two separate AC calculations, you can only pick one.
In other words, "Your Armor Class equals X" means it's an AC calculation, while "You gain a bonus to your armor class equal to X" means it's an AC bonus.