C.A.
If money is not a huge deal, I would buy your baby a ticket. Just because you can hold them on your lap does not mean it is safe, comfortable, and in the case of my squirming daughter, possible. We just got back from Hawaii and my husband did not want to buy her a seat. If we go anywhere else, I think I now have him convince a ticket will be purchased.
Bring snacks, sippy cup and little toys and books for him. Be cheerful and extra nice to the flight crew. They will be your best friends if you treat them kindly. One stewardess took my daughter up to first class to pass out flowers. Not only did that give me a break, it changed the scenery for my daughter. Another airline employee gave us a whole row to ourselves on the trip home. These small 'favors' really helped us travel.
I would call the airline and let them know that you have a lap baby if you decide to hold on to him. I did that when we made our reservations and therefore they had the correct number of passengers. I would also bring a copy of his birth certificate. The airline, over the phone, said that I needed it but they never asked for it. At the same time, I was glad I had it so there was no confusion over the fact that she could be a lap baby.
Go to the airport extra early so you are not in a rush and can get through security without being frantic. Put his snacks and sippy cup in a clear plastic gallon sized baggy so that when you need to have it in a security bin, you are not having to collect small bags and pieces.
Good luck!