Combine pesto and lemon juice in small bowl. Evenly brush beef steak with 1 tablespoon pesto mixture.
Place steaks on grid over medium, ash-covered coals. Grill, covered, 11 to 15 minutes (over medium heat on preheated gas grill, 13 to 16 minutes) for medium rare (145°F) to medium (160°F) doneness, turning occasionally.
Meanwhile, preheat oven to 425°F. Spray 10 x 15-inch rimmed baking sheet with cooking spray. Place dough on baking sheet and pat dough to edges of baking sheet. Spread dough with remaining 3 tablespoons pesto mixture. Top with tomatoes and cheese. Bake in 425°F oven, 15 to 18 minutes or until crust is golden brown.
Carve steak into slices; season with salt, if desired. Top pizza evenly with arugula and steak slices; sprinkle with red pepper, as desired.