The story: The political gridlock in Lebanon has come to an end with the election of Gen. Joseph Aoun as president and the appointment of lawyer Nawaf Salam as premier. The election of Aoun, who is backed by Saudi Arabia and the US, and the naming of a prime minister opposed by Hezbollah indicate the Iran-backed group’s diminishing clout.

While Hezbollah remains a major force, a loss of its political influence would be a setback for Iran, which is already grappling...