Combine the ground lamb, shallot, capers, basil and pepper in a large bowl and mix well. Divide mixture into four burgers. Spread cornmeal(or flour) over a plate and press burgers into the mixture to coat. Preheata barbeque(or broiler) and brush with oil. Cook the burgers over a medium high heat for 6-7 minutes each side or until cooked as desired.
To make the relish:
Place the tomatoes and onion into a preheated saute pan with the olive oil. Cook for 5 minutes. Add sugar, vinegar, salt and pepper. Remove from the heat and let cool. Grill the buns(or broil), cut side down, until lightly toasted. Spread with goat cheese and top with the burgers. Serve with the tomato relish. Enjoy!