Pat the salmon fillets dry with paper towels. This helps the skin get very crispy. Place them on a clean baking sheet. Brush both sides with olive oil now.

Sprinkle salt and pepper over the salmon fillets. Strip the leaves off the fresh thyme sprigs. Press the herbs onto the top of the fish. This helps the flavors stick well.

Slice the Meyer lemons into thin round circles. Remove any seeds you see in the fruit. These will be grilled alongside the salmon pieces. They look great and add juice.

Place the salmon skin-side down on the grill. Close the lid and cook for six minutes. Do not move the fish during this time. This creates beautiful grill marks on it.

Flip the salmon fillets over very carefully now. Place the lemon slices on the grill too. Cook everything for another four to five minutes. The salmon should be opaque inside.

Remove the salmon and lemons from the heat. Place them on your large serving platter. Squeeze the warm grilled lemons over the fish. Serve it immediately while it is hot.