Lebanon 2 was a bit of a disaster for Israel. They lost heavily on the ground and they found they had no real answer to Hezbollah's rocket fire against Israeli cities. Hezbollah by all accounts now seems to be much better equipped than it was in Lebanon 2. It could be Israel is just desperate for Lebanon 3 to come along, but I rather suspect not,
Jerusalem suburb of Even Sapir evacuated as wildfire spreads (Haaretz)
from the article: Hezbollah 'refused Hamas request to bomb Israel in Gaza war'