Preheat oven to 450 degrees F. Put your pizza stone in the oven if you have one.
Put the sliced red onion in a small bowl and stir in the lime juice. Add salt and pepper to taste and set aside, stirring every few minutes so that they all get pickled.
Lightly flour a square of parchment paper. Roll out the dough with a rolling pin to about 12 inches.
Use your hands to spread about 1 tablespoon of olive oil all over the dough, especially the edges. Use a flat baking sheet or a large cutting board to transfer the parchment paper and the dough to to oven. If you have a pizza stone, great, otherwise put the parchment paper directly on the rack.
Set a timer for 1 minute, then remove the parchment paper and pizza dough and put it on the counter.
Spread the Sweet Chili Sauce all over the pizza, leaving a crust if you want. Sprinkle 1 cup of cheese on top. Add the chicken or pork and distribute evenly. Add the zucchini slices and shredded carrot.
Stir the pickled onions one last time, and add them to the top of the pizza, leaving the remaining lime juice behind.
Transfer the pizza and parchment paper to the oven rack or pizza stone, and bake for about 8 minutes, or until the cheese is melted and some of the carrots have just started to brown.