In a medium bowl, mash tuna with 2 tbsp (30 mL) mayonnaise. Add pickles, celery, 1 tsp (5 mL) lemon zest, 1 tbsp (15 mL) lemon juice, salt and dill. Add egg and mix until combined.
In a large skillet, heat half of canola oil over medium-high heat. Add tuna to hot oil by the spoonful. Press lightly to flatten. Patties should be about 2 in. (5 cm) in diameter and about 1/4 - to 1/2 -in. (5 mm to 1 cm) thick.
After 5 to 7 min., flip patties over, add more oil, if needed, and cook until golden brown. When patties are nearly ready, top with cheese, cover, reduce heat and let cheese melt.
Spread dinner rolls lightly with mayonnaise. Add cucumber slices, hot tuna patties and serve.