Hi, and hugs. I'm not T1 so can only give limited info. I would keep on at the health professionals because levels above 15 are not good. Have they told you about testing for ketones in the blood? I'm assuming babies are at risk for that like older kids and adults are.
Unfortunately, (as you will know) when someone has high BG they are more prone to infections, which increase the BG. It's a vicious cycle, that's why it's so important to get the BGs down.
Maybe a T1 can advise, but I thought it was possible/usual to get the BG down to a somewhat safe level after diagnosis before discharging the person from hospital? 19.8 seems way too high to just be coping with at home with Lantus. (To the T1s
Could having a different insulin added, or switching completely help?
Don't be afraid to take him to A&E if he is really struggling, as they may be able to monitor him and give him meds that help, and it will show the diabetes team how hard things are for him. Even being on an IV drip can help a person feel better.
I would also keep an eye out for symptoms of meningitis... I don't know if that's a big issue in the UK but it is in NZ. The doctors here would always rather children of this age are brought in if they have possible signs of it, as better safe than sorry.
I hope things improve soon as it will be very tiring for both bubs and for you.