I think it's important to note who the lobbyists are trying to speak for: it's you as a voter. Same with money.

Bottom line: you cannot buy a political office anywhere in America. You still must be voted in. You also cannot directly give money to a politician for their personal benefit; money can only be contributed to their (re-)election campaign. It's valuable because it buys media (that's 60% or more of a campaign cost).

So money, and lobbyists, are just proxies for large blocks of votes.

To fix this problem, you really need voters who stand by their own principles and aren't overly influenced by one-sided media (that's the only reason a politician needs money).

You also need to somehow disconnect the influence of media and advertising from actual voters. Would love to hear ideas on that particular problem.

More realistic changes include those that Lessig proposes: finance campaigns through what is effectively a capped tax credit offered to every taxpayer to allocate among candidates as they see fit, then repeal Citizens United.