Heat grill to medium-high. Place chicken in large bowl. Finely grate zest of lemon over chicken. Add scallions, parsley, 2 Tbsp oil, ½ tsp salt, and ¼ tsp pepper and toss to combine. Squeeze lemon juice over top and toss again.
Choose a veggie combo and, in second bowl, toss vegetables with remaining Tbsp oil and ¼ tsp each salt and pepper.
Thread chicken and veggies onto skewers. Grill, turning occasionally, until chicken is just cooked through, 8 to 10 minutes.
