Process first 10 ingredients in a food processor until smooth, scraping down sides as needed. Form mixture into 12 (2-inch) patties about 1/2-inch thick. Dredge patties in flour, shaking off excess.
Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium heat.
Add 6 patties; cook 3 minutes on each side or until lightly browned.
Remove from pan; keep warm. Repeat procedure with remaining 1 1/2 teaspoons oil and patties.
Arrange lettuce, cucumber, tomato, and green onions on serving plates. Top servings with falafel patties.