Heat 1 teaspoon oil in a nonstick skillet over medium heat. Add corn, and cook until tender, about 3 minutes. Remove from heat. Stir in onion. Let cool.
Whisk together lemon juice and sugar. Drizzle in remaining tablespoon plus 2 teaspoons oil, whisking until combined.
Combine corn-onion mixture, chile, crabmeat, and basil. Gently stir in lemon dressing, salt, and pepper. Cover, and refrigerate until chilled, at least 30 minutes (or up to 2 hours). Serve garnished with basil leaves.