2 tablespoons (1/4 stick) butter
10 ounces fresh crabmeat
1 tomato, seeded, chopped (about 1/2 cup)
1/3 cup plus 3 tablespoons chopped fresh basil
2 garlic cloves, minced
1/2 cup all-purpose flour
1 1/2 cups clam-tomato juice (such as Clamato)
1 cup whipping cream
1/4 cup ketchup
1/4 cup bottled clam juice
2 teaspoons Old Bay seasoning
1/4 teaspoon hot pepper sauce
3/4 cup water
2 tablespoons fresh lemon juice
Melt butter in heavy large pot over medium-high heat. Add 3/4 of crabmeat, tomato, 1/3 cup chopped fresh basil, and garlic. Sauté 2 minutes. Whisk in flour; stir 2 minutes. Whisk in clam-tomato juice and next 5 ingredients. Reduce heat to low and simmer until slightly thickened, about 10 minutes. Cool soup slightly.
Puree soup in batches in blender until smooth. Return soup to pot. Stir in 3/4 cup water and lemon juice; bring to simmer. Season with salt and pepper. (Can be made 1 day ahead. Chill uncovered until cold, then cover and keep refrigerated. Bring to simmer before continuing.) Divide soup among 6 bowls. Sprinkle with remaining crab and 3 tablespoons basil and serve.