Lay 1 tortilla flat. Fold 1/3 up over center. Spoon 1/6 of the filling across the doubled portion, leaving a 2-inch border at each end. Roll tortilla once, fold in ends, then roll snugly to enclose filling. Secure seam with toothpicks. Repeat to fill remaining tortillas.
In a 5- to 6-quart pan (at least 10 inches wide) or 14-inch wok over high heat, bring about 1 inch oil to 360 degrees, adjust heat to maintain temperature.
Using a wide metal spatula, lower 1 chimichanga at a time into hot oil, filling pan without crowding. Fry until golden on all sides, turning occasionally, 6 to 8 minutes total per chimi. Transfer to a towel-lined 10- x 15-inch pan. Keep warm in a 225° F oven. Repeat to fry remaining chimichangas.
Meanwhile, peel, pit, and thinly slice avocados. Moisten slices with lime juice. In a 1- to 11/2-quart pan over medium heat, warm chili sauce; pour into a small bowl.
Line a platter or plates with lettuce. Remove toothpicks from chimis and place, seam down, on lettuce. Sprinkle chimis evenly with 1 cup cheese and garnish with avocado. Serve with remaining cheese and the chili sauce, sour cream, and salsa, to taste.
Makes: 4