Drain tuna, add to a medium-sized mixing bowl, and mash with a fork; stir in mayonnaise and lemon juice.

Remove crusts from bread and flatten with a rolling pin until about 1/16-inch thick.

Spoon tuna in a log down the middle of each slice of bread.

Peel and grate 1 carrot and finely dice 1/2 of a cucumber. Add to the tuna and roll up the bread tightly to enclose the filling. Cut each roll crosswise into four pieces.

Peel the remaining carrots and cut into sticks; slice the remaining cucumbers; remove seeds from melon and cut into cubes.

Serve tuna roll-ups with veggies and melon on the side.