If I were Israel, here is what I would do: I would extend an offer to Lebanon that basically says "If you allow us, we will come into your country, remove all Hezbollah terrorists and then assist you in rebuilding your infrastructure as long as you agree not to allow the terrorists back in."
There seems to be some support in Lebanon for the current mission that Israel has undertaken. Many in Lebanon are scared of Hezbollah and the armed militants and would like to see them removed. Israel has the power to do that and then assist the Lebanese government in stabalizing the country and keep terrorists groups out by providing military protection of Lebanon's border.
If Israel extended such an offer, that would put Lebanon in a checkmate position with two really tough choices. They could accept Israel's offer for the betterment of the country but they would alienate themselves from Iran and Syria. But, the country would prosper eventually from stability and world support. Hezbollah would be gone and the citizens of Lebanon would be much safer.
Or they could reject the offer which will lead to the destruction of their country. Let's face it, Lebanon was barely hanging on to begin with...they are going to be left in total chaos after this. The country could find itself back in another civil war when Israeli strikes are done and I don't see Iran or Syria really helping fix it. The world won't want to be involved because it's only Lebanon. Israel will back one faction, Iran/Syria will back another and the country will suffer for the next 20 years.
Either way, if Israel were to make sure an offer, it would look good to the world. There is some rumor out there that the Lebanese government knew the attacks were coming and actually supported them because of their fear of Hezbollah and their hope to remove the terrorists from the country. If Israel can work an agreement with the Lebanese government similar to the one I outlined, the region and the world would benefit. A stable Lebanon makes everyone a winner (except Syria and Iran).