Often humans respond to being sick with increased liver production of glucose. For most adults, this raises our fasting blood sugar and raises our basal insulin needs. And being sick also is about inflammation. Our bodies naturally respond to inflammation with increased insulin resistance. As to why, that is complicated, but many people think it is a result of increased stress hormones (like cortisol) and possibly the effect of macrophages (the bodies cells that fight infection). Although most adults have to markedly increase their basal and bolus, kids are more complicated.
Insulin does not kick in all at once, it is absorbed. For a modern rapid insulin this happens over perhaps 5 hours. And absorption is increased with activity due to improved blood flow and increased metabolism.
Since you found that decreased Lantus caused morning highs, then to a first degree you know that (at least overnight) your Lantus is at a reasonable level. Since you are really concerned, perhaps you should both advance the meal boluses and increase the ICR. If your son is using an ICR of of 20 grams/unit, then increase that to 25 or 30 and see if that reduces the after meal lows.
ps. I am assuming your son is not on medication.
pps. If your son has had digestion problems that can make it more complicated.