Cook the fettuccine or spaghetti according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute, until fragrant but not browned.
Reduce the heat to low and stir in the heavy cream, allowing it to warm through for about 2 minutes.
Add the grated Parmesan cheese, lemon zest, and lemon juice to the skillet. Stir until the cheese is melted and the sauce is smooth.
If the sauce is too thick, gradually add the reserved pasta water until you reach your desired consistency.
Season with salt and pepper to taste. Add the cooked pasta to the skillet and toss to coat evenly with the sauce.
Serve immediately, garnished with fresh parsley.