For the Chicken: Whisk together lemon juice, olive oil, kosher salt, pepper and thyme. Pour over chicken breasts in nonreactive bowl (such as a stainless steel one, but not one made of aluminum). Cover and marinate in refrigerator 6 hours or overnight.
Heat a charcoal grill and cook chicken for 10 minutes on each side, until just cooked through. Refrigerate and chill. Slice breasts diagonally into 3/8-inch-thick slices.
For the Salad: Toss chicken plus its juices, lemon juice, olive oil, sugar snap peas, red and yellow bell peppers, lemon slices, salt and pepper in a bowl. Taste for seasonings and serve cold or at room temperature.