In an emailed statement, Jay Dardenne says the state "has the infrastructure in place to maintain their record-breaking program."
Dardenne authored the state's film and TV tax credit program. He says he'd use his influence in the state's industry to help the Robertsons.
The network suspended patriarch Phil Robertson last week for comments he made to GQ magazine about gays.
Dardenne says that regardless what people think about Robertson's comments, the program has drawn a huge audience eager to visit Louisiana.
The lieutenant governor's job includes running the Department of Culture, Recreation and Tourism.