Position a rack in the upper third of the oven; preheat to 400 degrees F. Put the squash in a large microwave-safe bowl with 1/4 cup water; season with salt and pepper. Cover with plastic wrap and pierce a few times with a knife to vent; microwave until tender, 8 minutes. Drain and pat dry. Whisk the eggs and 1/4 cup water in another large bowl until frothy.
Heat 2 tablespoons olive oil in a medium nonstick ovenproof skillet over medium-high heat. Add the chorizo and cook, stirring, until it just starts browning, 3 minutes. Add the squash, bell pepper and garlic. Cook, stirring occasionally, until the pepper is tender and the squash starts browning, 5 minutes. Stir in the scallions and cook 1 minute. Transfer to the bowl with the eggs using a slotted spoon; stir.
Wipe out the skillet. Coat the bottom with 2 tablespoons olive oil and heat over medium heat. Add the egg mixture and spread in an even layer. Cook until the edges are golden, 5 minutes. Transfer the skillet to the oven and bake until just set in the center, 12 to 15 minutes.
Toss the arugula with the remaining 1 tablespoon olive oil and the lemon juice; season with salt and pepper. Loosen the edge of the frittata and unmold onto a plate; cut into wedges. Serve with the salad.