Maybe next time you're at the barn, you can ask what he's eating? It's good to be involved and aware of every aspect of your horse's care.
If his weight is okay, there isn't a need to add more calories to his diet. Most likely he is lacking "umph" because barrel racing is a new job to him and he isn't properly conditioned yet. You say he is in shape, but he may not be in shape for barrel racing. I tried to barrel race my endurance horse and it almost killed her!
If some workout sessions he is more lethargic than others, he may be tired from his last workout and isn't bouncing back fast enough. Over training a horse is dangerous and can result in injury. What does his conditioning program look like?
If he is running out of energy midway through a training session, he's probably being pushed too hard at his currently fitness level and needs shorter, lighter sessions with more walking breaks.
Also, speed isn't everything. It wears and tears at the body. A horse only has so many sprints in them. Slow work with focus on technique is much better in the long run in every respect.