Preheat the oven to 400 degrees F. Whisk the eggs in a large bowl with 1/4 cup water, 1/4 teaspoon salt and a few grinds of pepper. Stir in the crushed tortilla chips and let soak 5 minutes.
Heat 1 tablespoon olive oil in a 10-inch nonstick ovenproof skillet over medium heat. Crumble in the chorizo and cook, stirring, until no longer pink, 3 to 4 minutes. Add the scallion whites and cook until softened, 1 to 2 minutes. Spread the chorizo evenly in the bottom of the skillet and pour the egg mixture on top. Top with the cheese and bake until the eggs are browned around the edges and a knife inserted into the center comes out clean, 12 to 14 minutes.
Meanwhile, combine the lettuce, radishes, scallion greens and cilantro in a large bowl. Drizzle with the lime juice and the remaining 2 tablespoons olive oil; season with salt and pepper and toss. Slide the frittata onto a cutting board; sprinkle with cilantro. Slice into wedges and serve with the salsa and the salad.