In a small bowl, whisk together the oil, mustard, lime juice, salt, pepper, and Italian seasoning.
In a large serving bowl, combine the lettuce, cucumber, red onion, grape tomatoes, olives, and bell peppers, if using. Cover and place in the refrigerator until ready to serve.
Place the onions and carrots in the slow cooker.
Pat the chicken dry and place it on top of the onions and carrots. Pour melted butter over the top of the chicken. Squeeze lime juice all over the top of the chicken. Season evenly with salt, pepper, garlic powder, thyme, paprika, and any other seasonings. Cook on low for 3 ½ - 4 hours or until chicken is cooked to 165 degrees F.
Allow to cool slightly and then shred the chicken, serving 1 cup of chicken with the carrots, onions, and salad with dressing and Feta cheese.
Store the remaining chicken in an airtight container in the refrigerator for up to 3 days or in the freezer for up to 6 months.
Save the bones and skin in a resealable bag or airtight container in the refrigerator or freezer for chicken stock later.
Strain the chicken broth/stock from the bottom of the slow cooker and store in an airtight container in the refrigerator for up to 3 days or in the freezer for up to 6 months.
