1. Drain tofu. In large bowl, use your hands to crumble tofu, breaking it up into small pieces.
2. Grate carrot until you have about 1 cup; squeeze to remove excess liquid. Add carrot, seasoning, and oats to crumbled tofu, stir until well combined. Form into four balls and pack together tightly. Flatten into thin patties.
3. In fry pan, heat oil over medium-high heat. Cook patties until golden brown, 3–4 min per side.
4. Meanwhile, cut cheese into eight slices. Slice tomato and onion.
5. Remove patties from pan and set aside. In the same pan, fry cheese until golden-brown, about 1 min per side.
6. Divide half the lettuce leaves on plates; cover with patty, cheese, tomato, and onion slices, then remaining lettuce.