Heat the olive oil in a medium saucepan over medium heat; add the garlic and cook for a minute. Add the cream, the lemon zest and juice, salt and pepper. Bring to a boil, then lower the heat and simmer for 10 minutes, until it starts to thicken.
Meanwhile, add some salt to the boiling water and add the pasta; cook according to the directions on the package, stirring occasionally.
Drain the pasta and place it back into the pot. Immediately add the cream mixture and cook it over medium-low heat for 2-3 minutes, until most of the sauce has been absorbed in the pasta.
Take the pot off heat and add the spinach, Parmesan, and tomatoes. Toss well until the spinach has wilted. Season to taste, and serve hot.
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