The role of a lieutenant governor typically includes several responsibilities, but among the options provided, the most accurate choice would be:
- to cast the tie-breaking vote in the state legislature.
Lieutenant governors often serve as the president of the state senate and have the authority to cast a vote in case of a tie. They may also assume the governor's responsibilities if the governor is unable to serve, but the option about the tie-breaking vote specifically highlights a key function of their role in the legislative process.