edit: just noticed the 'has to eat' is he on mixed insulin since that does require a certain amount of carbohydrates as does using a fixed dose of rapid insulin with meals. (cutting carbs with a mixed insulin is difficult, with rapid you will have to be able to adjust the dose of the rapid; and possibly the basal See my second book suggestion)
A ketogenic diet as used for epilepsy has to be supplemented in order to provide sufficient vitamins and minerals . Children often need more than adults
http://site.matthewsfriends.org/uploads/factsheets/Vitamins and minerals.pdf
The site also holds a collection of relevant papers. As you can see, it is not without problems but can help these children with intractable epilepsy
http://site.matthewsfriends.org/index.php?page=medical-papers
What though do you really mean?
If you mean by a LCHF diet your son is veering towards a diet of eggs, cheese , meat and added fats as demonstrated by one exponent
here then personally I would think that he was very unlikely to be getting sufficient nutrients.(and certainly very little fibre).
For the reasons below I wouldn't tell him this was bad I would though try to encourage far more plant foods.
If he is eating lots of vegetables, some dairy (calcium is important during adolescence/twenties as that is when bone grows) protein and some fruit, perhaps nuts and seeds then it's more likely that he will be getting sufficient.
(there are of course carbohydrates in most of the above,)
If he wants to take part in activities that depend on a quick supply of energy then he may find he needs more carbohydrate.
Have a look on the
runsweet site for info about this.
From my reading ( I am a T1, and a parent but not of a T1) I would be wary of reinforcing the idea that any food or food group is bad for people with T1 diabetes (except perhaps for things like full sugar coke ) Yes we have to be careful not to eat high glycemic refined foods but so should everyone.
There are young people with diabetes that find that a continual focus on food, and the necessity to inject and test leads them to want to get control back by reducing food and or eating without testing or injecting
I think that it is far better to learn how to manage different foods in different situations so that they can eat similarly to their peers when necessary (yes, unfortunately sometimes junk foods ), whilst for the most part having a basically sound nutritious diet.
This means gradually learning how foods affect him and bow to use insulin, to try to mimick a pancreas. It won't come overnight . It won't be straightforward (diabetes is never totally predicable) but feeling in control rather than being controlled by diabetes is I think important and allows flexibility. (important in the teens and twenties)
I know this is beyond the scope of your question but if you haven't seen them then these 2 books might be helpful.
http://www.amazon.co.uk/Type-1-Diabetes-Children-Adolescents/dp/185959350X (the 'bible' for many parents and written in an adolescent friendly style)
http://www.amazon.co.uk/Think-Like-Pancreas-Gary-Scheiner/dp/0738215147/ref=sr_1_1?s=books&ie=UTF8&qid=1409405672&sr=1-1&keywords=think like a pancreas
