sounds like he’s a typical 4 year old arabian. you might just have gotten a more “hot” arab.
I have an 8 year old who is just full of spunk and my mom has an 11 year old who is an old pokey butt. It’s just the personalities. He might relax some as he ages. He might always be a more high strung/high energy horse. Keeping his mind busy will help as well. Give him things to do in the pasture. We used to set up barrels in the pasture and put them in different patterns and then hide treats/hay around them so the horses would have to figure out how to get to the goodies. Some horses love playing with toys too.
If possible I would do something more than just lunging him. That is just boring work for a horse. Mix it up, have him do figure 8’s, touch things with his nose, step up onto things, put some logs down, etc. Keep his brain working, don’t let him go into autopilot.(which a lot of horses do when lunged)
"Take the time it takes, so that it takes less time."
"Expect a lot, accept a little, reward often."