Preheat the grill, clean and oil the grates well, prepare it for medium-high heat.
Prep the fish while the grill is preheating.
Wash the fish and pat dry (I usually have my fishmonger scale and gut the fish). Score both sides of the fish. Massage it with 1/2 tablespoon of olive oil and sprinkle both the outside and the cavity of the fish generously with salt and pepper.
Cut lemon and onion into thin slices. Stuff lemon slices, onion slices, and dill into the cavity of the fish.
When the grill is ready (remember it needs to be hot), place the fish on the grill and let it cook for 5-6 minutes.
When the fish no longer sticks to the grates, it's time to flip. Use a spatula to slide under the fish and together with a pair of tongs, flip it. Cook for another 5 minutes (amount of time depends on how big your fish is).
When the fish is fully cooked, transfer to a serving plate and follow the steps I mentioned earlier to cut it. Drizzle lemon caper sauce over it and enjoy.
For the lemon caper sauce
While the fish is cooking, put all ingredients to make the sauce into a bowl and mix well to combine.
If you don't have fresh herbs on hand, you can sprinkle dried Italian herbs generously into the cavity of the branzino.