Those readings certainly are very high & concerning. It points to doses being too low.
I take the same insulin’s and Lantus should cover 24hrs if the dosage was correct. With the morning reading being 250 (9mmol) this is still too high & I would be going back to the doctor who would most likely increase the dose by 2 every couple of days.
When you say he changed pens a couple of months ago do you mean he switched to a different insulin? Because if the same pen is used for months this could be a problem, once you break the seal on a new pen it should be used within 28 days, if not it could go off.
With readings that high I would also be checking for ketones and if they were present I’d seek urgent medical help.
Testing & recording really is key here, it needs to be before & 2hrs after every meal plus tracking what he is eating as the nova rapid will cover a certain amount of carbs and anything over that will continue to raise levels.
Regarding the needle, I would remove it each time & use a fresh one with every injection. This significantly limits the risk of infection but I receive free prescriptions from the NHS. Depending on how many times the needle is reused it may be blocked or not hitting the right spot when injecting so he may think he’s using 22u of Lantus but not all of it might be absorbed.
There may be good reasons why he is reusing needles but it certainly is risky.