Preheat the oven to 350 F. Heat the olive oil in a skillet with the diced onion and garlic. Sauté until the onions become translucent. Then add the paprika, chili powder, cumin, and sea salt and stir to coat. Remove the skillet from the heat.
Add the pulled chicken to the skillet and toss with the onion mixture until the chicken is somewhat coated in the spices. Squeeze the lime half over the chicken to stir in the juice.
Pour 1 ½ cups of the enchilada sauce over the chicken and stir to coat. Set aside.
Wash each zucchini and trim off the top and bottom. Use a vegetable peeler to cut thin slices of zucchini. Place each slice on a paper towel. When done peeling, place another paper towel over top and press down gently to remove any excess water from the zucchini strips.
Lay three zucchini slices down on a clean flat surface and overlap slightly. Add three tablespoons of the chicken mixture at the top of the strips. Use your thump to hold the chicken in place while you pull the top of the zucchini strips over the chicken and continue to roll up. Place each zucchini roll up inside of a 9 X 13 baking dish. You should be able to fit two rows of 8 - 10 roll ups in the dish.
Pour the remaining enchilada sauce over top of the roll ups and sprinkle with dairy free cheese. Bake in the oven for 20 - 30 minutes until the cheese has melted and the zucchini is soft.
Top with cilantro leaves, avocado slices, and dairy free sour cream if desired and serve.