Use a kitchen towel or paper towels to pat dry the pressed and cubed tofu. In an 8×8-inch baking dish or shallow bowl, arrange the tofu pieces in a single layer. Set aside.
In a small bowl, whisk together the lemon juice, 2 tablespoons olive oil, Dijon mustard, garlic, oregano, thyme, salt, and black pepper until well combined. Adjust seasoning to taste.
Pour the marinade over the top of the tofu, turning the pieces to coat. Marinate for at least 1 hour, and up to overnight, turning once.
Set a large skillet over medium-high heat and add the remaining 1 tablespoon olive oil. When the oil is hot, use a slotted spoon to transfer the tofu to the pan, keeping the pieces in an even layer. Cook for 7-8 minutes, turning occasionally until golden brown on all sides.
Add any remaining tofu marinade and continue cooking for an additional 1 minute. Serve hot, cooled to room temperature, or cold.