1. Place first 5 ingredients in a food processor; process until smooth. Heat a large nonstick skillet over medium heat. Add 2 teaspoons oil to pan; swirl to coat. Add 4 (1/4-cup) batter mounds to pan, pressing each with the back of a spatula to flatten slightly. Cook 4 minutes on each side or until golden and thoroughly cooked. Remove from pan; keep warm. Repeat procedure with 2 teaspoons oil and remaining batter. Sprinkle fritters with 1/4 teaspoon salt.
2. Combine remaining 1 tablespoon oil, remaining 1/4 teaspoon salt, lemon juice, and black pepper in a large bowl, stirring with a whisk. Add arugula, cherry tomatoes, cucumber, and onion; toss gently to coat. Arrange about 1 cup salad, 2 fritters, and 1 tablespoon goat cheese on each of 4 plates. Serve immediately.