Make the Herb Mayonnaise: In a medium bowl, stir together garlic, mayonnaise, lemon juice, basil, dill, mustard, salt and pepper.
Make the Salmon Sandwiches: Brush grill with wire brush to remove any crumbs or crusty bits, then preheat grill for direct grilling over medium-high heat.
Pat salmon fillets dry with paper towel. Rub salmon generously on all sides with oil, and then sprinkle with salt and pepper on all sides.
Spray grill grates throughly with cooking spray. Place salmon directly on grill grates. Cover grill and cook 4 to 6 minutes or until fish is beginning to turn opaque.
Using a heatproof spatula, carefully flip fish. Cover grill and cook 4 to 6 minutes longer or until internal temperature in the thickest part of the fish reaches 125 degrees F. Remove salmon from grill and let stand 5 minutes before building sandwiches.
To serve, spread both halves of buns with Herb Mayonnaise. Divide lettuce over bottom halves of buns. Place 1 piece of salmon on each sandwich and top with top halves of buns. Serve immediately.