Finely dice the celery (enough for 1 cup) and slice the green onion. Combine the tuna, celery, green onion, walnuts, mayonnaise, lemon juice, salt, and pepper in a bowl. Stir until everything is evenly combined.
Cut the remaining celery into sticks. Cut each mini sweet pepper in half and scoop out the seeds.
Divide the tuna salad between four containers (about 1 cup each). Add celery sticks, mini sweet peppers, and crackers (wrapped in plastic wrap) to each box with the tuna salad. Refrigerate the lunch boxes for up to 4 days.