“black market” argument could be made for pretty much any law

Not the OP, but ... murder or genocide is very clearly a crime, while lobbying starts with "talking to an elected official about laws that concern you", which is sorta normal in democracy, the elected officials should be available to talk. It only becomes problematic if it is overdone or done too secretively.

I think that a good and transparent lobby register is probably more useful than outright ban; at least an external observer can glean some information from it.