IME you have to call because they need to have your lap infant on the manifest for the flight. Even when traveling with my child with his own ticket, they had to document that he was in a car seat.
Even if it isn't their protocol, personally I would call to cover all my bases.
We travel Southwest a lot and need to call ahead to give the information of the lap baby to them. They require name, date of birth and gender usually to put in the system. And in case of more than 1 adult traveling, they ask which adult will have the lap baby on their ticket.
I flew Southwest this past December with a lap child and I didn't have to call ahead. I did have to check in at the counter and show them his birth certificate.