What if the HRE Frederick I Barbarossa won a decisive and devastating victory over the Lombard League, allowing him to dissolve many of the privileges of the Northern Italian states, creating an intermediary authority, a sort of "Exarchate of Ravenna"-like realm whose leader is directly appointed by the Holy Roman Emperor?
Could a puppet state in northern Italy, with relative autonomy but a single leader appointed by the King of Germany, allow the HRE to retain Lombardy?