Lebanon is in a precarious situation, torn between Israel and Iran, with its current government being the first in many years where the Shia militia group Hezbollah has relatively low influence. The government is worried about being taken hostage by Iran, and there is a constant fear in Lebanon that a new civil war will break out. Iran and Hezbollah will do everything to try to sink any conceivable agreement with Israel and are absolutely prepared to go to war to prevent it from happening, though both Iran and Hezbollah are currently weakened, as is the Lebanese state.
If Iran were to follow through on its threats to attack Israel as punishment for Israel's attack in Lebanon, it would be interpreted as a victory for Hezbollah, and Iran would then retain its grip on Lebanon, with Hezbollah demanding an increasingly larger share of power. Israeli Prime Minister Benjamin Netanyahu announced late Thursday that Israel is open to talks with Lebanon, with preparations underway from both sides and delegations expected to meet in Washington on Tuesday. Several details remain, the most important being that Lebanon demands at least a shorter ceasefire if there is to be any meeting at all, while Israel appears to be under pressure from the US to de-escalate the situation in Lebanon, though so far, the Israeli side does not want to use the word 'ceasefire'.
What Lebanon hopes for is a ceasefire agreement similar to the one the US concluded with Iran earlier in the week, leading to an agreement on a list of starting points for further negotiations. A major question for the Lebanese government is who will take responsibility for the reconstruction of all villages and communities that have been completely destroyed by Israel during the fighting against Hezbollah, as after the war between the same parties in 2006, Gulf states stepped in and covered the cost, but it is not likely that this will happen now. The biggest question for Israel is that Lebanon ensures the disarmament of Hezbollah, which the Lebanese government also wants, but it is something that will require large investments in the Lebanese defense forces, and it would require help from many other countries for the Lebanese army to have a chance against the Shia Muslim militia group in a confrontation.
No Lebanese government wants to end up in an active dependent position towards Israel, and agreeing to a deal directly with the Israeli government would be seen as a huge betrayal by a large part of Lebanon's population, though this alternative is seen as safer if the US can guarantee that it means the Israeli army leaves Lebanese territory.