Heat 1/4 cup olive oil in a large saucepan over medium heat. Fry rabbit pieces in hot oil until evenly browned. Season with bay leaves, salt, allspice berries, oregano, and lemon juice to the saucepan. Pour white wine over the rabbit. Bring the mixture to a simmer; cook 4 to 5 minutes. Add enough water to the saucepan to cover rabbit completely.
Bring the liquid to a simmer; cook until rabbit is cooked through and the water is evaporated, about 40 minutes.