In small bowl stir together lime juice, soy sauce, sugar and crushed red pepper. Set aside.
In nonstick wok or large skillet stir-fry steak strips in 2 teaspoons hot oil over medium-high heat for 1 to 3 minutes or until hot. Remove from wok.
Add remaining 1 teaspoon oil, garlic and gingerroot to wok. Stir-fry for 30 seconds. Add broccoli, snow peas (if desired), bell pepper, carrot and onions to wok. Stir-fry for 2 to 3 minutes or until crisp-tender. Stir in strips and soy sauce mixture. Heat through. Serve over rice.