I was able to check in online with a domestic lap-child. It will usually ask you to indicate a lap child at time of check-in. If it doesn't, you will need to go to the desk. The infant doesn't get a separate boarding pass, just a note on your saying either "lap child" or "infant in arms".

I know that AA's kiosks also ask if you have a lap child when using them.

Without data on which airline, it is harder to answer