If using active dry yeast, dissolve it in about 3 tablespoons of the warm water along with the sugar and let it sit for 5 to 10 minutes until frothy. If using instant yeast, skip this step.
In a large bowl, combine the flour and salt. Make a well in the center and add the activated yeast or instant yeast, olive oil, and remaining warm water gradually, mixing until a soft dough forms.
Transfer the dough to a lightly floured surface and knead for about 10 minutes until smooth and elastic. Place the dough in a lightly oiled bowl, cover, and let it rise in a warm place for 1 to 2 hours, until doubled in size.
While the dough rises, prepare the topping by combining the ground lamb, onion, tomato, red and green bell peppers, garlic, tomato paste, red pepper paste, cumin, paprika, black pepper, and salt in a large bowl.
Mix thoroughly until well combined, then stir in the chopped parsley and lemon juice. The mixture should be thick and spreadable.
Preheat the oven to 450℉ and place an inverted baking sheet or pizza stone inside to heat.
Once the dough has risen, divide it into eight equal portions and roll each portion into a ball. On a lightly floured surface, roll each dough ball into a thin circle about 8 to 10 inches in diameter.
Spread a thin, even layer of the meat mixture over each dough round, gently pressing it into the dough with the back of a spoon.
Carefully transfer the prepared lahmacun to the preheated baking sheet and bake for 6 to 8 minutes, until the edges are crisp and the topping is fully cooked.
Repeat with the remaining lahmacun as needed, baking in batches. Serve hot with fresh parsley, lemon wedges, and a sprinkle of sumac.