Because a 'lap baby' doesn't get a seat, there is no reason to show them when booking seats for everyone else. That being said, you should be prepared to bring ID for your lap baby proving that he/she is entitled to be a lap baby.
I will say that many parents go into the whole lap baby thing with the hopes of getting an 'empty' seat for their child. That doesn't happen so often anymore. Flights are now full...and when you are flying on a flight where you have chosen your seats, prior to flight time, there is little chance your lap baby will have a seat, as there won't be an empty seat near you, and will be in your lap. I know of one person who booked a flight, and chose seats for her family of 6, with one being a lap baby. She chose three seats in one row, and the aisle and the window in the row behind them. Well...it was a very full flight, and someone saw that empty middle seat online and booked it. Imagine that mom's surprise when she boarded, with the hopes of having that empty seat for her lap baby, only to find a stranger seated between her and one of her kids!!! Evidently, the unknown woman was happy to move to the window seat, allowing the mom to sit next to her child.