Congress has some power to outlaw corruption (or the perception thereof), but not lobbying per se. Restrictions on donations to political campaigns have been upheld in the past, but those tend to be direct money donations to candidates.

Handing over money directly to a candidate is one thing, but the Courts have been a little more hesitant to uphold restrictions on lobbying or political speech -- and the spending of money to do it -- if it's being spent by or given to a third party not directly connected to the Government. The hesitancy is most recently exemplified in the Citizen's United case that is of significant controversy.

Sometimes I think that Congress had better think ahead to save its own skin, propose amendments to the Constitution about limits on corporations, before they lose all power to them and can no longer escape their grasp.

It's principal-agent problems all the way down.