For once, Israel is involved in a conflict where, if it's not clear that they are entirely in the right, it is at least clear that their opponents are in the wrong. Hezbollah's initial attack on and capture of Israeli soldiers had no visible provocation, and the possible motives, given the timing, seem to be selfish. The only possible beneficiaries seem to be Hasan Nasrallah, who improves his personal political standing among middle eastern Shiites, and Iran, which avoids U.N. Security Council sanctions by distracting the G8 meeting of heads of state in St. Petersburg.
That is not to say that Israel's behavior has been above reproach. Certainly shutting off sea and air access to all of Lebanon - forcing traffic to go by road through Syria, not an ally of Israel - seems unwise. Still, everyone seems to think that some response on the part of Israel was justified, and international criticism is unusually muted.
This leaves the Lebanese government in a difficult position. Without strong international pressure, Israel seems unlikely to cease bombing as long as Hezbollah continues to shoot rockets into Israeli territory. The Lebanese military is unable to control Hezbollah alone, and would certainly be no match for the Israelis, even if the Lebanese government were so inclined. The U.N. secretary general, Kofi Annan, is making noises about an international peacekeeping force, but the U.N. force already in Lebanon doesn't seem to have done much good. The situation doesn't leave the Lebanese government many choices.
There is one ray of hope, though. While Israel said, at the opening of hostilities, that they held the Lebanese government responsible for Hezbollah actions, they have now shifted to a more realistic view that Hezbollah is the enemy and not Lebanon as a whole. Israel doesn't particularly want to occupy the Hezbollah dominated areas of southern Lebanon - it didn't work out so well last time - so their ideal solution would be a Lebanese government strong enough and friendly enough to keep the peace in that area. That's a goal that the Lebanese government ought to embrace.
Lebanon's best approach would probably be to open direct negotiations with Israel. Not only would Israel prefer Lebanese government control to Hezbollah control in southern Lebanon, Israel may also be in a position to help make it happen. This solution would also avoid rewarding Hezbollah's violence, without disenfranchising the population of the area, as they would still be represented by the Lebanese government.
It won't be easy, but if it can be accomplished, it should leave everyone but Nasrallah better off.