I'm curious as to why you think Rove leaving had anything to do with Bush's decision to support Lebanon?
Bush has supported Lebannon all along.
Now without the political advisor/guru Rove warning about political consequences, there will probably be more swift and sure action in these situations and with Iran.
Rove did a good job as a political advisor and analyst. However, with him in the White House, every White House action or non action was evaluated and measured for political fallout or gain. That is probably gone now.