Prepare the Filling. In a large skillet, heat the olive oil over medium heat. Add the chopped onion and minced garlic, and sauté until the onion is translucent and fragrant.
Cook the Beef. Add the ground beef to the skillet, breaking it up with a spatula. Cook until the beef is browned and cooked through. Drain any excess fat if necessary.
Add Seasonings. Stir in the tomato paste, chili powder, cumin, paprika, oregano, salt, and black pepper. Add water to the skillet and mix well. Let it simmer for about 5 minutes until the flavors meld together and the mixture thickens slightly.
Prepare the Vegetables. While the beef is cooking, wash and separate the butter lettuce leaves. Dice the avocado, halve the cherry tomatoes, and thinly slice the red onion.
Assemble the Wraps. To serve, place a spoonful of the spicy ground beef mixture in the center of a lettuce leaf. Top with diced avocado, cherry tomatoes, and sliced red onion. Sprinkle with chopped cilantro.
Garnish and Serve. Serve immediately with lime wedges on the side for an extra burst of flavor.