The problem is that a corporation is legally defined to be the same as a person. A corporation has the same rights that a person does. Spending money is legally equivalent to speech.
Because of those two simple legal precedents, a corporation's right to lobby is literally protected by free speech.
I don't see the problem with corporations being equatable with people. They are composed of people. Just like unions, nonprofits, social clubs, political parties. Making money is their interest, but there is nothing criminal (or even morally wrong) about that.
The reason why corporations have disproportionate political power compared to other forms of human organization is because we fund elections via private donations, endebting our representatives to their donors before their constituents. And whoever controls the most money gets the most representation in our government. It should be possible for politicians to tell major corporations to fuck off without endangering their election, but it isn't. So even the most well meaning politicians take the money, give them a few votes on their pet issues, and then try to make the best with what's left.
Because of those two simple legal precedents, a corporation's right to lobby is literally protected by free speech.