This is really what they mean. "Lobbying" as a term generally connotes getting paid to do it. When people do it for free, it's more frequently called activism or advocacy.

I actually think a limit on pay might be better than an outright ban. Former members of Congress have skills, experience, and connections that could be beneficial for advancing a variety of social causes. It's the big payday, cashing-out part that stinks of corruption and undue influence.