In a small bowl, whisk together soy sauce, lemon juice, cornstarch, brown sugar, garlic and pepper, set aside.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat. Add beef and stir until almost cooked through, about 2 minutes. Transfer beef to a plate and cover to keep warm. Heat remaining oil in skillet, add onion and stir fry for 5 minutes.
Cut broccoli into florets (should yield about 4 cups) and add to skillet with 1/2 cup water. Bring to a boil, cover, reduce heat and simmer for 3 minutes.
Return beef to skillet with soy sauce mixture, add ginger. Bring to a boil and cook, stirring constantly, until sauce thickens, about 2 minutes. Serve over white rice or egg noodles.