A 15 month old probably does not want to sit in your lap. He wants to explore, especially at something as exciting as a football game.
I assume he walks and climbs? You may need to walk with him every 15 to 20 minutes. Just walk for a few minutes, but take him to a different section.
Will he still sit in a stroller? Roll him around the stadium, let him look at the band show him the cheerleaders and the mascot. If other people(that you know) want to hold him or carry him or walk around with them, let them. I know at my daughters high school, the coach and his wife have young children and the kids love taking those kids all over the stadium or sitting next to the coaches wife holding their children for practically the entire game. I noticed she has learned to enjoy this time by visiting with the other people around her.
At home he also will need to entertain himself a little more. Teach him how to do this. When you are doing something in the kitchen put him on the floor with a few toys or put the playpen close to where you will be, put some of his toys inside with him.
If I was mopping the floor or vacuuming and was worried about her being unsupervised I would sometimes put my daughter in her high chair with a wash cloth and have her "clean the tray" with the cloth. She loved doing this. Or I would put a paper bag with some of her toys in the bag and have her pull them out and then put them back in the bag. Sometimes, I would have a box with a lid, or an old purse. She loved seeing what was in the bag. I tried to not leave her in the chair for more than 15 minutes.
Just sounds like he is a true toddler not a baby anymore and is ready to move on to more active play and activities. He has watched his older brother and is ready to be as active as him.