Pour diced tomatoes and the juice into a heavy large covered casserole. Crush tomatoes. Add beef broth, 1/2 cup diced onion, brown sugar, one half of the minced garlic and 1 tablespoon lemon juice. Bring to boil. Reduce heat to low and simmer sauce while preparing meatballs.
Combine beef, breadcrumbs, salt, pepper, allspice, 1cup diced onion and remaining minced garlic in large bowl. Add beaten eggs; mix well. Shape into 1" to 1 1/2" meatballs. Gently place meatballs into the simmering sauce. Partially cover casserole and simmer over low heat until meatballs are cooked through and sauce is thick, approx 1 hour 30 minutes. Remove any fat that forms on top of the sauce.