What if Israel "flat-out" invades Lebanon in 1981? More specifically (since this is what the player aims for), Israel would seek to overthrow the government at Beirut, install the Maronites, and seek to force the Muslim populations of the country into Syrian-held areas and into Syria itself.
Now I'd imagine this would cause a war with Syria, vows across the Arab world to support the Lebanese Muslims (although I don't think Egypt would actually offer to fight Israel; not sure what Jordan would do), and the war itself would require far more troops than what Israel did IRL a year later, and become domestically unpopular.