Begin with the tuna salad. Combine ingredients in a large mixing bowl and stir to combine. Taste and adjust seasoning with salt and pepper.
Take cut bagels and toast under a hot broiler until golden brown. While still hot smear the bottom with the cream cheese immediately. Top with a scoop of the tuna salad and then layer with red onion, tomato, cucumber and lettuce. Add the top half of the bagel and serve.