Let's assume a Lizardfolk fighter, with the Defense fighting style, wearing leather armor. Lizardfolk, per Volo's p. 113, get Natural Armor:
You have tough, scaly skin. When you aren't wearing armor, your AC is 13 + your Dexterity modifier. You can use your natural armor to determine your AC if the armor you wear would leave you with a lower AC. A shield's benefits apply as normal while you use your natural armor.
Emphasis mine. Leather armor gives a DC of 11+Dex but, according to the above rule, I am allowed to use my superior Natural Armor DC of 13+Dex (this is different from mage armor and Draconic Resilience and which I almost asked about, but they specifically disallow wearing armor).
Now, at the same time, I'm wearing armor, which should qualify me for my chosen Fighting Style, Defense (PHB p. 72):
Defense: While you are wearing armor, you gain a +1 bonus to AC.
Emphasis, again, mine - it doesn't say anything about actually using the armor's AC.
Could I combine the two to claim an AC of 14+Dex?