Fill a large saucepan with enough water to cover chicken. Add garlic and bay leaf; bring to a boil. Place chicken in pan, and gently simmer until cooked through, 15 to 20 minutes. Use a slotted spoon to transfer chicken and garlic to a plate; let cool. Reserve poaching liquid.
Make dressing: Pulse garlic in a food processor to form a coarse paste, 5 to 10 seconds. Add 2 tablespoons reserved poaching liquid and the lemon juice, salt, and ricotta; pulse to combine. With machine running, add oil in a slow, steady stream, mixing until emulsified. Stir in dill, and season with pepper. Set aside.
In a medium saucepan, cover potatoes with cold water. Bring to a boil; cook until easily pierced with a paring knife, about 20 minutes. Drain, and let cool. Peel if desired, and cut into quarters.
Slice each chicken breast crosswise into about six strips. Divide lettuce, potatoes, tomatoes, and chicken among serving plates. Drizzle with some of the dressing, and serve immediately with remaining dressing on the side.