Preheat grill to medium heat. Clean and oil grill grates.
Marinate the chicken breasts in Italian dressing for 10 to 20 minutes while the grill heats up.
Toss the green beans in half the oil.
Brush the tops of the lemons with the other half of the oil.
Place chicken on grill, discard any additional dressing. Brush the chicken breast with half the teriyaki sauce, and cook the chicken for 4 to 6 minutes on one side. Flip the chicken breast over, and brush the other side with the other half of the teriyaki sauce. Cook for 4 to 6 minutes. Remove from grill and allow to rest for 5 to 10 minutes. Slice into thin strips.
Grill the beans or peas just long enough to char them, this should take 8 to minutes. Flip the over until they look perfect. Remove and set aside.
Grill lemons cut side down for about 3 to 5 minutes, flip and grill for about 2 more minutes. Remove and set aside.
Arrange the salad on a plate, platter, or bowl. Start with the lettuce, add the beans or snow peas, the onion and the strawberries. Toss chicken over top. Squeeze grilled lemon over top for flavour. Set some more lemons inside the bowl for anyone who wants more pucker.
You can add dressing if you like, but honestly this is divine just the way it is.
Enjoy with a big old grilled salad loving smile!