A composite article assembly arrangement includes mechanized assembly station tooling for supporting certain composite article assembly methodologies with a view toward a preferred lid assembly application. First assembly station tooling includes a stationary main base plate, opposed intermediate compactor plates, and opposed outer plates, which compactor plates and outer plates are movable relative to the stationary main base plate. One or more continuous webs bearing thermoformed first and second workpieces are directed through the mechanized assembly station tooling, which operates to both separate the first and second workpieces from the web(s) as directed therethrough and assemble the first and second workpieces in one clapping movement of the compactor plates and outer plates relative to the main base plate. Alternative assembly station tooling operates to direct first composite elements into assembled relation with stationary second composite elements for forming basic composites to which successive composite elements are similarly added.