It cannot be said too often that the word republic is derived from res publica, which is Latin for general welfare, the public good or the common wealth. Consequently the principal aim of a republican government is to pursue public rather than private interests.
Lobbying is, according to Wikipedia, to attempt to influence the decisions made by government officials. In scientific literature one will find that political scientists distinguish different types of lobbying. Here we will distinguish two types: white and black hat lobbying.
The purpose of white hat lobbying is to further the public good. Human rights activism is an example of this type of lobby.
On the other hand black hat lobbyists seek to bend political decisions in such way, that their private interests (rather those of who hire them) rather than the public good.
It is obvious that the second type of lobbyism is at odds with the very core of classical republicanism. After all the government does not exist to promote the private interests of certain factions of society, at the cost of others.
Therefore a republican society needs strict regulation of lobbying in order to prevent that private interests will undermine the public good. Since lobbying undermines the very foundation of republican government, lobbyists who violate the rules should not be dealt with mercy. They have to be expelled from society, to be deported to a penal colony.