Place the side of salmon in a large ziplock bag and pour the marinade over the fish. Turn a couple times to coat and place in the refrigerator for at least 1 hour and up to 4 hours.
Heat a grill to medium/high heat. Remove the salmon from the marinade. Lay the lime slices directly on the grill, spaced to create “a rack” underneath the salmon.
Place the salmon, skin side down, on the lime slices. Close the grill and cook the salmon until just cooked though and the center is a little darker pink for medium rare.
Keep a careful eye on the salmon toward the end of the grilling time. The skin and lime slices could catch fire and cause the salmon to burn. Watch your flame!