Place salmon on a work surface, and remove any excess fat. Feel for any small bones, and remove with tweezers or a strawberry huller. Place salmon flat on a large glass baking dish. Rub salmon with oil; sprinkle with sea salt and next 3 ingredients.
Squeeze juice of 1 lime over salmon just before cooking. When the grill is hot, place salmon flesh side down, and cook, undisturbed, about 6 minutes or until salmon releases from grill easily and is golden brown on the cooked side.
Turn salmon over, and place it skin side down on a piece of heavy-duty aluminum foil (cut longer than the fish). Squeeze juice from remaining lime over salmon, and cook, covered with grill lid (or additional foil), 6 more minutes or until fish starts to flake. Lift salmon in aluminum foil from heat, and let rest, loosely covered, about 5 minutes before slicing. (It will continue to cook slightly.)
Remove skin before serving. Serve warm or at room temperature topped with Cucumber-Avocado Salsa.
Wow! What a great meal. This recipe was very good and easy to make. For Father's Day it was perfect. We made the recipe as directed and it turned out to be a 4 star meal. The salsa really complemented the salmon and I would make this again.