Cook the fettuccine according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a large skillet, heat the olive oil over medium heat. Season the salmon with salt and pepper, then add it to the skillet. Cook for about 4-5 minutes on each side, or until the salmon is cooked through and flakes easily with a fork. Remove the salmon from the skillet and set aside.
In the same skillet, add the cherry tomatoes and garlic. Sauté for about 3-4 minutes until the tomatoes are softened.
Flake the cooked salmon into bite-sized pieces and return it to the skillet.
Add the cooked fettuccine, reserved pasta water, basil, Parmesan cheese, and lemon juice. Toss everything together until well combined and heated through.
Serve immediately, garnished with additional basil and Parmesan if desired.