This is a basic grilling method for producing just-cooked salmon with a crunchy skin for your eating enjoyment. Or, you can remove the skin easily after grilling for those who choose not to partake. Use this to practice and gain confidence in your own grilling expertise.
Preheat your gas grill or light a medium-hot charcoal fire (350-375 degrees F). When ignited and heated, put the grill cover on for about 15 minutes with the cooking grate. Remove the cover and scrape the grate thoroughly clean.
Remove the fillet from the refrigerator and place it on a baking sheet. Sprinkle the salt evenly all over the fish.
Place the fillet skin side down over the hottest part of the grill. Arrange the lemon slices around the fish. Cook until the bottom of the fish starts to change color, about 5 minutes. Turn the lemon slices to grill the second side and remove to a platter when grill marks appear.
Place the grill cover back on to retain the heat (turning the grill into an oven) and cook the topside of the fish. Check the fish in 3 minutes. Some of the white albumen will begin to appear, but it will still be less cooked at the thickest part.
At 125 degrees F, the salmon will be medium-rare, which some people prefer. If you are not one of them, return the cover and cook the fish for 2 to 3 minutes more. Don't be shy about using the spatula to cut into the fish if you are at all uncertain.
The flesh will be firm to the touch and there will more of the white albumin visible all over the fish. At 135 degrees F, the fish is completely cooked, but it is best to remove the fish at 130 degrees F--or a minute or two before completely cooked--because the residual heat will finish the cooking off the grill.
At this point the skin will be very crisp, nearly charred in places, and release easily from the grate. Slice a spatula underneath the fillet all around just to check. Then, with a second spatula, lift the fish onto the platter with the lemon slices and serve with your chosen accompaniments. (If using the flavored butter, as pictures, place pats of butter along the filet while it's still hot.)
Many people grill salmon with olive oil. I don't find it necessary, except when I want to add that flavor, because the fish is so deliciously fatty on its own. And, sticking is never an issue with this method. That said, go ahead and oil the fish, if you'd like.