1. Marinate chicken
Finely chop 1 teaspoon garlic. In a medium bowl, combine 2 tablespoons each of yogurt, water, and oil, 2 teaspoons garam masala, 1 teaspoon salt, ½ teaspoon of the chopped garlic, and a few grinds of pepper. Pat chicken dry, then transfer to marinade, turning to coat. Set aside until step 3.
2. Prep cucumber relish
Preheat broiler with rack in top position. Finely grate ¼ teaspoon lemon zest into a medium bowl, then squeeze 1 tablespoon lemon juice into a small bowl. Trim ends from cucumber, then peel and halve lengthwise. Finely chop cucumber. Finely chop roasted red peppers.
3. Broil chicken
Remove chicken from marinade and transfer to a rimmed baking sheet lined with foil; discard any remaining marinade. Broil on top oven rack until chicken is browned in spots and cooked to 165°F internally, 8–10 minutes (watch closely as broilers vary). Transfer to a cutting board to cool slightly.
4. Make cucumber relish
While chicken broils, add cucumbers, roasted red peppers, remaining chopped garlic, and 1 teaspoon oil to bowl with lemon zest, tossing to combine. Season to taste with salt and pepper.
5. Make tahini sauce
Add tahini and 3 tablespoons of the remaining yogurt to bowl with lemon juice. Stir in ¼ cup water and 1 tablespoon oil to make a smooth sauce (if too thick, add 1 tablespoons water at a time, as needed). Season to taste with salt and pepper.
6. Prep lettuce & serve
Trim stem end from lettuce and separate leaves. Slice chicken into strips. Assemble lettuce wraps at the table, filling lettuce leaves with chicken, cucumber relish, and a drizzle of the tahini sauce. Enjoy!