Drain the tuna well. Finely dice the celery 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.
Slice 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 to each box with the tuna salad. For extra protection, either wrap the crackers in a sandwich baggie or pack them separately. Refrigerate the lunch boxes up to four days.