Mix 1/4 cup soy sauce, fish sauce, ginger, and garlic together in a large bowl. Stir in beef cubes. Marinate in the refrigerator for at least 1 hour and up to overnight.
Preheat oven to 275 degrees F (135 degrees C).
Place flour in a shallow bowl. Strain beef into the flour; toss to coat. Reserve marinade.
Heat peanut oil and 1 teaspoon sesame oil in a large wok or skillet over medium-high heat. Add beef cubes; saute until browned, 3 to 4 minutes. Transfer to an oven-safe plate and place in the oven to keep warm.
Cook eggs in the same wok until scrambled, about 2 minutes. Stir in reserved marinade, 2 tablespoons soy sauce, 1 teaspoon sesame oil, and Chinese five-spice powder; cook for 1 minute. Stir rice gradually into the wok until evenly distributed. Pour in tomato sauce; cook and stir until heated through, about 4 minutes.
Whisk lemon juice, salt, and pepper together in a bowl. Divide evenly among 4 dipping cups.
Serve beef with rice, lemon juice, and chopped onion.