Toss the beef with 1 tablespoon each cornstarch and vinegar and 2 teaspoons soy sauce in a medium bowl. In another bowl, stir the brown sugar, the remaining 2 teaspoons each cornstarch and vinegar, the remaining 1 teaspoon soy sauce, and 1/3 cup water until dissolved.
Heat 1 tablespoon olive oil in a large nonstick skillet over high heat. Add the beef and cook, stirring occasionally, until just cooked through, 2 to 3 minutes. Transfer to a bowl and wipe out the skillet.
Heat the remaining 2 tablespoons olive oil in the skillet over high heat. Add the garlic and red onion and stir-fry 2 minutes. Add the mushrooms, chard stems, 1/4 teaspoon salt, and pepper to taste and stir-fry until the vegetables are just tender, 4 minutes. Add the chard leaves and stir-fry until wilted. Stir the brown sugar mixture and add to the skillet along with the beef, stirring, until thickened, 1 minute. Add the lemon juice and season with salt and pepper. Serve with rice.
Per serving: Calories 300; Fat 15 g (Saturated 3 g); Cholesterol 41 mg; Sodium 561 mg; Carbohydrate 13 g; Fiber 2 g; Protein 28 g