Combine crabmeat, tomatoes, lemon zest, lemon juice, pepper, 1/2 cup parsley, 1/4 cup oil, and 1 tsp. salt in a large bowl.
Cook spaghetti in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 1 cup pasta cooking liquid, and add to crab mixture. Stir vigorously and add pasta cooking liquid and oil as needed to fully coat. Season with salt.
Transfer pasta mixture to a serving bowl or platter and top with remaining 2 Tbsp. parsley. Serve immediately.
