For the quarter-century since the World Trade Organization began operating, Robert Lighthizer has been calling it “a threat to sovereignty” and a hotbed of “judicial activism,” hamstringing America’s efforts to counter its economic rivals, especially China.

Mr. Lighthizer, who is now President Trump’s U.S. trade representative, will soon be able to claim a victory in his long battle against the organization. The WTO was formed to resolve international trade disputes through multilateral rules and institutions, originally with...