In a food processor, purée the avocado and lime juice until smooth. Season with salt and pepper. Cover and refrigerate until ready to serve.
In a large bowl, combine 1 tbsp (15 ml) of the oil with the remaining ingredients and mix thoroughly. Season with salt and pepper. Working with lightly oiled hands, shape the mixture into 8 small patties.
In a large non-stick skillet over medium-high heat, brown the patties in the remaining oil for 4 minutes, turning halfway through cooking.
Spread the buns with the avocado mixture and layer with the lettuce and tuna patties. Top with the cucumber.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.