We kinda need lobbying and it would be very hard to effectively criminalize it. It would just move father into the back rooms. When I say we need it, groups like the EFF, NAACP, FFRF and ACLU all have lobbying arms.
A different idea proposed by Lawrence Lessig would be to remove elected officials from the legislative branch and replace it it something like the Jury Duty system from the court systems. While not perfect, it would be much harder to bribe a constantly rotating group of civilians and most people will vote in their interest even when it’s against their party alignment on a case by case bases.
Lobbyists would become like courtroom lawyers either pushing for or against certain laws in a public settings.