Whisk the olive oil, lemon juice, salt, pepper, dried herbs, onion powder, and smoked paprika together in a small bowl.
Place the chicken breasts in a large resealable bag, pour the marinade over, seal, and massage to coat. Refrigerate 30 minutes, or up to 4 hours.
Arrange the chicken in the air fryer basket in a single layer. Cook at 400°F for 15–20 minutes, flipping halfway, until the internal temperature reaches 165°F. Rest 5–10 minutes before slicing.
Place the 4 eggs in the air fryer basket. Cook at 260°F for 17 minutes.
Transfer the eggs immediately to a bowl of ice water for 1–2 minutes, then peel under the water.
Slice the rested chicken into ½-inch strips.
Divide the almonds, grapes, and cheese pieces between four sectioned containers, then divide the chicken between them.
Add one egg per box, whole or halved and seasoned with salt and pepper.
Lid the containers and refrigerate up to 3 days.