Rinse the fish under cold water and pat dry with a paper towel. Deeply score the outside of the fish three times on each side. Season inside and out with salt and pepper. Cut three of the lemon slices in half and set aside. Stuff the cavity of the fish with the fennel fronds and remaining lemon rounds. Close the fish and slide a halved lemon round into each of the score slits.
To wrap the fish in the grape leaves, lay it on one side and shingle the leaves over the side of the fish facing you, leaving some overhanging over the top. Delicately flip the fish, so now it’s leaf side down, and repeat shingling on the other side of the fish until it’s fully wrapped. (It’s okay if some fish skin is still exposed.) Use 3 or 4 pieces of kitchen twine, depending on the length of the fish, to wrap around the fish and tie a knot. Tuck the leaves under the string as best as you can to create a little wrapped package. This will help keep the fish together while grilling. Fish can be prepared up to 4 hours ahead of time and kept in the refrigerator. Allow the fish to temper for 30 minutes to 1 hour before grilling.
Prepare your grill to medium heat.
Drizzle olive oil over the grape leaves, using your hands to rub it around. Lay the fish perpendicular to the grill gates and cook for 8 to 10 minutes on each side, depending on the size of your fish. The grape leaves help to keep the moisture in and steam the fish, so you have some wiggle room. Once the first side is charred and the fish has released itself from the grill, use two metal spatulas to delicately flip the fish over to finish cooking on the other side. Use a paring knife to check the meat along the spine of the fish for doneness.
Cut the string and squeeze over fresh lemon juice to serve.