Combine lemon zest, lemon juice, oil, oregano, salt and pepper in a large bowl. Reserve 2 tablespoons of the marinade in a small bowl. Add tomatoes, mushrooms, zucchini and onion to the remaining marinade; toss well to coat. Thread the vegetables onto eight 10-inch skewers. Drizzle the vegetables and steak with the reserved marinade.
Grill the steak 4 to 6 minutes per side for medium. Grill the vegetable kebabs, turning frequently, until tender and lightly charred, 8 to 12 minutes total. Remove the vegetables from the skewers and serve with the steak.