In a small bowl, dissolve the sugar and yeast in warm water. Let it sit for about 10 minutes until frothy.
In a large mixing bowl, combine the flour and salt. Make a well in the center and add the yeast mixture and olive oil. Mix until a dough forms.
Turn the dough out onto a lightly floured surface and knead for about 5-7 minutes until smooth and elastic. Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm place for about 1 hour, or until doubled in size.
In a large mixing bowl, combine the ground lamb or beef, finely chopped onion, minced garlic, chopped tomato, chopped parsley, tomato paste, ground cumin, paprika, ground cinnamon, ground black pepper, salt, and red pepper flakes (if using). Mix well until all ingredients are thoroughly combined.
Preheat your oven to 450째F (230째C). If you have a pizza stone, place it in the oven to heat up.
Punch down the risen dough and divide it into 8 equal pieces. Roll each piece into a ball and then roll out each ball on a lightly floured surface into a thin round, about 8-10 inches in diameter.
Place the rolled-out dough on a parchment-lined baking sheet or a pizza peel if using a pizza stone. Spread a thin layer of the meat mixture evenly over the dough, leaving a small border around the edges.
Bake in the preheated oven for about 8-10 minutes, or until the dough is crispy and the meat is cooked through. If using a pizza stone, slide the parchment paper with the lahmacun onto the stone and bake.
Remove the lahmacun from the oven and place on a serving platter. Serve hot with lemon wedges for squeezing over the top.
Enjoy your meal!