[bunderbunder]

In this context, "lobby" doesn't just mean petitioning the government. It specifically means when you have someone whose full-time job is to try and influence legislators and other policymakers on behalf of one's employer.

In the early USA it was considered antithetical to democracy precisely because it gives a great advantage to people with the financial resources to hire a lobbyist. So for over 200 years now, the word "lobbying" has already had a particular definition in the context of the money=speech debate. I don't think that trying to redefine the the term in the way you propose makes your point so much as it hinders it by muddying the waters.