Mix together the lime juice, 2 tablespoons of the basil and salt and pepper to taste in a shallow, non-metallic dish. Add the salmon fillets and turn them in the mixture to coat well all over. Cover and leave to marinate in a cool place for 30 minutes.
Meanwhile, mix together the yogurt, mayonnaise, lime zest and remaining basil in a small bowl. Season with salt and pepper to taste. Cover with plastic wrap and refrigerate until required.
Preheat the grill to moderate and preheat the oven to 160 degrees C. Lift the salmon fillets out of the marinade (reserving the marinade) and place on the foil-lined grill tray. Brush with a little of the reserved marinade, then grill for 4–5 minutes on each side or until the fish is just cooked and the flesh is beginning to flake, brushing again with the marinade after you have turned the fillets. While the fish is cooking, place the bread rolls in the oven to warm through.
Split the bread rolls in half and spread the cut sides with the basil mayonnaise. Put a cooked salmon fillet on the bottom half of each roll and scatter over a few mixed salad leaves. Place the top half of each roll in place and serve immediately.