I’m not sure why some are being so harsh on the OP, and I will side with them here.

I have two kids, one still young enough to fly as a lap child. While it is certainly true that there is no ticket needed for a lap infant flying on domestic flights, typically, they are added to the reservation, and get their own BP. I don’t know specifically if there is a UA policy requiring them to be added, but I would think they’d want to know and have that info in the manifest, especially as some aircraft have seating restrictions for flyers with a lap infant (for example, CRJ/7 require lap infants on the A/B side, and there are only 4 seats on the E45s where they can sit, both due to these being the only locations which have an extra oxygen mask). I’d think weight and balance could come into play as well (especially during the holiday season where you have many more lap infants traveling.

In addition, while TSA doesn’t require ID for anyone under, I think, 12, Id think, but don’t know for sure that they’d need some sort of doc to get through security. Like I said, UA has always printed BPs for lap infants when we travel.