Preheat the oven to 375°F (190°C).
In a large skillet, heat the olive oil over medium-high heat. Add the crumbled tofu, garlic, lemon juice, oregano, salt, and pepper. Cook for 10-15 minutes, or until the tofu is crispy and golden brown.
While the tofu is cooking, prepare the tzatziki sauce. In a mixing bowl, combine the vegan yogurt, grated cucumber, garlic, lemon juice, dill, salt, and pepper. Mix well and set aside.
Warm the pita bread in the oven for 2-3 minutes.
To assemble the gyro, spread a generous amount of tzatziki sauce on each pita bread. Add a layer of shredded lettuce, diced tomato, sliced red onion, and the cooked tofu. Roll up the pita and serve.