The Hizbullies population resides in certain parts of Lebanon but mostly in Beirut. You destroy those areas only and The Christian militias, The Druze militias, and the Sunni militias will take revenge on Hizbullies all by themselves. The sparkplug would be knocking out the Lebanese power grid. If there are further attacks from Lebanon, just take over South Lebanon and move all the population out. I bet you get a peace treaty in less than 3 months.