To prepare souvlaki, combine 3 tablespoons lemon juice, olive oil, 4 garlic cloves, oregano, 1/2 teaspoon salt and pepper in a zip-lock plastic bag; seal and shake to combine. Add chicken to bag; seal and shake to coat. Marinate chicken in refrigerator for 1-2 hours, turning once.
Remove chicken from bag; discard marinade. Thread the chicken onto each of 4 (8-inch) skewers.
Heat a grill coated with cooking spray over medium-high heat. Add skewers; cook 8 minutes or until chicken juices run clear, turning once.
To prepare tzatziki sauce, combine yogurt, 1 tablespoon lemon juice, 1/4 teaspoon salt, and 1 garlic clove and cucumber in a small bowl; stir well. Serve the tzatziki sauce with chicken souvlaki for dipping.