Wash the whole lemon under running water, dry thoroughly, and freeze in a freezer-safe container until firm, about 4 hours or overnight.

Bring a large pot of water to a boil and salt it. Cook spaghetti according to its package until al dente, usually 10–12 minutes. Reserve 1 cup cooking water before draining.

Finely grate 2 teaspoons of yellow peel from the frozen lemon, stopping before the thick white pith. Keep fingers away from the grater; return the remaining lemon to the freezer.

Combine olive oil and 1/4 cup pasta water in a wide skillet over low heat. Add drained spaghetti and toss for 30 seconds. Remove from heat.

Add Parmesan gradually while tossing, followed by grated lemon and pepper. Add reserved water a tablespoon at a time until the sauce coats the strands. Taste before adding more lemon or salt. Finish with parsley and serve immediately.