You could swap “taxes” for “regulations” in your last sentence and it’d be equally true - scrapping corporate taxed wouldn’t eliminate corporate lobbying.
True, the more overregulated an economy is, the more corrupt it will be. That's just a fact of life. Corollary, the less regulated countries but with a strong rule of law for the few regulations that do exist are the less corrupt worldwide. Note that it is easier to have strong and consistent application of the law (rule of law) when regulations are fewer as it's more simple to handle for both the legislator and corporations which increase the level of trust and lowers corruption.