With a lap infant on a domestic flight, you do NOT have to inform them before arriving at the airport; however, you will need to get a boarding pass for the infant and have them flagged on your ticket, which you have to do at the check-in counter (can't do kiosk or online check-in). In fact, you may not want them on your itinerary prior to check-in since it will likely prevent you from doing online check-in. So in this case, especially due to the uncertainty, and if you want to do OLCI (for higher priority boarding), I would suggest you NOT add them to your itinerary until you get to the airport, and just plan that you will have to stop at the counter to get the infant boarding pass. Also the airline may want to do age verification (<2) in person so make sure you have a passport or birth certificate.

I just did this last week on Southwest with my infant; in addition I signed him up with his own mileage account because Southwest policies are that once he is in their system as age verified once by their staff, I will then be able to check him in online as a lap infant in the future - but not sure if this is feasible or useful in your case.