Combine avocado, lime juice, and sea salt in a small bowl and mash with a fork. Stir until mixed thoroughly and set aside.
Warm a burrito-sized tortilla in the microwave between two paper towels for about 20 seconds. Transfer to a plate or large work surface to assemble the burrito, then preheat a cast iron griddle over medium heat for toasting the burrito later.
Assemble the burrito. First, spread the mashed avocado over the tortilla, leaving some room around the edges. Then add the chopped steak and fries in a line down the center of the tortilla. Top with shredded cheese and pico de gallo.
Fold the burrito. Fold in opposite sides at each end of the filling until the edges are almost touching in the center, then hold the ends closed with both hands while using your thumbs to fold one of the remaining sides over the filling. Keep holding the ends closed and roll the burrito over itself to close.
Transfer the burrito to the preheated griddle and toast until lightly golden-brown, using a grill press if you have one, about 1 to 2 minutes on each side.
Transfer burrito to a cutting board and slice in half. Serve immediately with a side of chips and salsa.