Air-defence systems can't drop bombs on rebels, or do air policing over areas where the government may not have the clout to install ground-based air defence systems.
You appear to assume that fighters must be for use against external enemis, but I think the Lebanese government wants them for internal use.
Unless you're talking about Fateh el-Islam or some other Palestinian group operating inside of Lebanon, the Lebanese Army can't go against any type of insurgency inside their territory, especially Hezbollah (if that's what you were talking about). The Lebanese gov't is already (and has been for a long time now) in a very weak and uncertain position. I doubt bombing their own country to target a highly influential group such as Hezbollah will do any help.
You can't use warplanes to crush an insurgency or militia group. Just ask Israel and the US. If anything using warplanes might even weaken their position because of the civilian casualties often associated with the use of warplanes in civilian areas.
The Lebanese Army is just under-equipped and uses outdated equipment. That's why they couldn't take care of the Fateh el-Islam issue fast enough. Not because they lacked warplanes. I think attack helicopters are better suited for this role.
Buying a credible air-defense system to protect the people in the south from Israel will strengthen their position by showing that the military is capable of defending the country and take away from the legitimacy of groups like Hezbollah and show that groups such as Hezbollah are not needed to defend the nation against Israeli aggression.
The air-defense system is still the best option. Politically speaking, militarily speaking and economically speaking. I also think that Hezbollah will look really bad not allowing an air-defense system made to defend the nation to be installed or let in on their "turf". And Nasrallah has been calling on the Lebanese Army and the UN to find a way to stop Israeli overflights on Lebanon (which are meant to gather intel on Hezbollah). An air-defense system might put an end to Israeli recon flights on Hezbollah. So there is an interest for them in this too.
A credible air-defense system will do everybody involved in the situation (except Israel) some good. I'm sure that the interests involved for both parties will make Hezbollah and the Lebanese gov't come to a compromise regarding an air-defense system in the South of Lebanon.
