Pat salmon dry. Brush caesar dressing over fish. Cover and refrigerate 1 hour, turning once.
Coat grill rack with oil. Place fish on grill.
Grill, brushing with fresh caesar dressing and turning once, just until fish begins to flake when tested with a fork, about 8-10 minutes on each side.
To serve, cut salmon steak in half. Toss lettuce with caesar dressing and parmesan cheese. Place salmon steak on bed of dressed lettuce. Add desired amount of croutons.