Bring a large pot of salted water to boil. Prepare a large bowl of ice water; place a colander inside, resting in ice.
In batches, stir spinach into boiling
water. Cook until wilted and bright
green, about 30 seconds. Transfer spinach
to the colander (in the ice bath)
to stop cooking. Reserve boiling water.
Cool completely in ice bath, then lift
colander; squeeze spinach dry.
Cook pasta in reserved boiling water until al dente, according to package instructions. Save 1/2 cup pasta water; immediately drain pasta, and return to pot.
Meanwhile, place spinach, Parmesan, walnuts, garlic, and lemon zest and juice in a food processor. Process until a coarse paste forms. With motor running, add oil and 1/4 cup plain water; process until smooth and creamy, about 1 minute. Season with salt and pepper.
Add tomatoes and pesto to pasta; toss, adding reserved pasta water to coat pasta, if necessary. Taste and adjust salt and pepper, as needed. Serve with additional Parmesan, if desired.