One particular focus for Dickstein during the Mackinac Island event was to urge Republican attorneys general like Ms. Bondi not to join an investigation into marketing claims used by 5-Hour Energy, according to several people who attended the event but asked not to be named because the conversations were supposed to be confidential. The inquiry was initiated in early 2013 by more than 20 states.

Image Ms. Bondi Credit... Eve Edelheit/Tampa Bay Times, via Associated Press

Ms. Kalani, other partners at Dickstein and their clients also donated money directly last year to a Florida campaign group run by Ms. Bondi. It included a $10,000 payment from ETC Capital, an investment fund controlled by the owner of the 5-Hour Energy brand, as Dickstein Shapiro sought to ensure that Florida did not join the investigation into the company.

The invitation to stay at Ms. Bondi’ s home in Tampa came after Ms. Kalani showed up at the Michigan resort with a foot injury, according to two people who attended the event. Ms. Bondi urged Ms. Kalani to consult with her own physician in Florida. After Ms. Kalani did so, Ms. Bondi invited her to stay as she recovered from surgery.

Dickstein Shapiro may be violating Florida law by failing to register as a lobbying firm, given the nature of the appeals it has made to Ms. Bondi and her office, which include advocating policy on issues that are important to its clients, instead of just legal matters, said Charles H. Rose III, a professor at Stetson University College of Law in Gulfport, Fla. At the request of The Times, Mr. Rose reviewed copies of emails that firm executives had sent to Ms. Bondi’s office.

“Law firms engaging the attorney general on general policy matters, as opposed to a specific client issue, should register as lobbyists,” Mr. Rose said. He pointed in particular to the unusual dual role of attorney general as both a law enforcement official and a member of the so-called Florida Cabinet, making decisions regarding the operation of Florida state government.

Neither Ms. Kalani nor Bernard Nash, a lawyer who leads the Dickstein Shapiro practice that focuses on state attorneys general, is licensed to practice law in Florida, according to the Florida Bar. As such, Mr. Rose said, it would be hard to see how they could argue that they were working solely on legal matters when communicating with Ms. Bondi and her staff.