BRUSSELS—The European Parliament on Tuesday lifted the immunity of the former president of Spain’s Catalonia region, Carles Puigdemont, and two of his associates, a move that could pave the way for their extradition and reopen the scars of separatism in Spain. The Spanish government immediately welcome the decision by the European Union’s legislature as a victory for the rule of law and against those who sought to break the rich northeastern region away from the rest of Spain. The decision will likely also extend the 3 1/2-year legal saga on the fate of the three separatists by months, if not years, since many avenues for appeal remain open before any possible extraditions. In the decision on Puigdemont, 400 legislators voted for the waiver of immunity, 248 were against and 45 abstained. The measures to lift the immunity of his associates—former Catalan Health Minister Toni Comín and former regional Education Minister …