In an extra-large skillet, heat coconut oil over medium-high heat. Add tofu, mushrooms, shallot, chile pepper, lemongrass, salt, and black pepper. Cook, stirring often, until mushrooms are cooked and shallot are transparent, 8 to 10 minutes.
Transfer tofu mixture to an large bowl and let cool until slightly warmer than room temperature, about 15 minutes. Stir lime zest and juice, mint, and cilantro into the tofu mixture. Serve larb in leaves.
Tip: To press a block of tofu, wrap the block in a dish towel and place on a rimmed plate. Place a cast-iron skillet on top or other heavy object on top; let tofu drain for 20 minutes. This can be done up to 24 hours ahead of time.