Israel does have a powerful lobby. They are not a complete puppet. They do things for our security state, so they can exert leverage. The US establishment also

Israel does have a powerful lobby. They are not a complete puppet. They do things for our security state, so they can exert leverage. The US establishment also is fine with Israeli lobbying because they want to maintain that relationship as an outpost and a place they can outsource certain intelligence operations to. It's kind of a virtuous cycle that is very much more dependent on US imperialist designs than it is on Israel.