Lobbying is "directly advocating for or against particular legislation or regulations." Writing your representative is lobbying. Fighting bad legislation is lobbying. Any good faith attempt to argue a position on a government policy is lobbying.

Giving money to politicians or their campaigns is not lobbying, and it is already illegal for lobbyists to do so.

What could and should be made illegal is allowing unlimited political campaign donations via Super PACs. Political donations aren't lobbying.

It's worth being clear about what you actually want to make illegal because you probably don't want to ban anyone from arguing a political position.