The Israel Lobby is a blanket term covering several Jewish organizations in the US, including AIPAC, all of which support a Likud policy platform. That would include Zionists of America, American Jewish Committee, and now the Anti-Defamation League, and many others.

I'm not certain what complications you might be referring to, apart from oil and the false notion that Israel provides a base of operations for Americab Middle East diplomacy, Israeli lobbyists have made certain that US politicians follow the Israeli line, whatever it may be. You need only appreciate the response in Congress to the Mavi Marmara incident, where even VP Biden repeated the usual hogwash, that "Israel has a right to defend itself."