Combine the red onion, cilantro, and lime juice in a small bowl, and set aside.
Fill a medium pot with water, salt generously, and bring to a boil. Add the cubed sweet potatoes, and cook for 15 minutes, or until the potatoes are fork tender throughout. Remove from heat, drain the water, and return the potatoes back to the pot, stirring in the butter, salt, cumin, paprika, and cayenne (if using). Allow to cool for 10 minutes, then mash in the avocado.
Working with one warmed tortilla at a time, rub the halved lime across the top, then spread a heaping tablespoon of the potato and avocado mash onto the side closest to you. Top with a 1/2 tablespoon of the onion and lime mixture, then gently roll the tortilla away from you, so that the filling is secured inside. Insert a toothpick to help the taquito hold its shape while cooking.
Heat 1/4” of olive oil in a large skillet over medium heat.
Working in batches of 4-6 at a time, fry the taquitos, using tongs to rotate and cook them evenly on all sides, 4-5 minutes total. Remove the toothpicks once finished cooking.
To serve, spread the shredded lettuce across a platter, then stack the taquitos on top, garnishing with the cherry tomatoes, sliced Fresno chili, additional cilantro, and lime wedges. Sprinkle with cotija, and serve with a bowl of Creamy Avocado Dip.