The problem and his strategy are laid out in his (free CC-licensed) book The USA is Lesterland: http://lesterland.lessig.org/ As with all big ideas, that requires a bit more time to digest than a HN comment. Plus, he's a better writer than I am.
The main idea of his PAC is if political bills can only happen in our system with the approval of 'Big Money', you need Big Money to pass the reform that would get rid of Big Money's influence. Hence, you need a PAC that gets involved in specific races and puts pressure on candidates who don't support the changes they're pushing for.
On a more broader level, Lessig is one of the big names in a loose coalition pushing for a constitutional convention that would amend the Constitution to overturn Citizen's United. The neat thing about such a convention is it's a checks-and-balances way that the popular vote can effectively by-pass their congressional representatives. This has happened only once before: http://en.wikipedia.org/wiki/Convention_to_propose_amendment...
This can happen if 2/3's of states agree to participate. California just passed a "we're in" bill a few days ago, joining Vermont. Similar bills are pending in other states: http://www.sfgate.com/politics/article/California-seeks-cons...
This is actually one of the few non-partisan issues that both sides can agree on. Well, the constituents of both sides... most representatives hate this idea, which is exactly why you need a well-funded PAC to exert influence onto them.