In a 4-quart saucepan, bring 3 quarts of water to a boil over high heat. When the water boils, reduce heat to simmer until you’re ready to cook the pasta (step 5).
While the water is heating up, use a grater to take off small peels of the skin of one lemon into a small saucepan. Cut the lemon in half and squeeze the juice into the pan and remove pits. Use the back of a large spoon to press the inside of the lemon to extract more juice. Add the garlic and 1 tablespoon of the olive oil to the saucepan. Stir to blend well. Place on stovetop on low heat.
Heat a large nonstick pan or grill pan on high temperature until very hot. Sprinkle the scallops with salt, pepper, and 1 tablespoon of olive oil. Toss to coat well.
Place the scallops in the hot pan. Cook about 4 minutes on each side, or until scallops are well browned and firm and milky white to the center (to a minimum internal temperature of 145 °F).
After turning the scallops to the second side, drop the pasta into the boiling water. Set temperature on medium, and cook for 2 minutes or the shortest recommended time according to package directions.
When the pasta is done, set aside ½ cup of the cooking water. Drain the pasta. Return drained pasta to the pot, and toss with the warm olive oil mixture and the ½ cup reserved pasta water.
Divide the pasta equally among four plates (about 1 cup per plate). Top each with four scallops.
Garnish each dish with ½ tablespoon of shredded parmesan cheese. Serve immediately.