Simple geography: Goulburn is an inland city in the Southern Tablelands of New South Wales, ~195 km (121 mi) from the nearest coast (Batemans Bay). Lighthouses exist to warn ships of coastal hazards—rocks, reefs, headlands. Goulburn has no navigable waterway requiring maritime signaling.
The confusion might stem from Goulburn River (Victoria) or Goulburn Islands (NT)—both coastal. But Goulburn, NSW? Purely a wool, rail, and government town—no lighthouse needed, none exists.