This gets stranger indeed
The first two bits, is the lantus, saying that it's 3ml, as lantus and glarine are the same, the 3ml is the cartridge size being used (not a vile which is 10ml)
The next bit is basically the strength of the insulin all insulin that is supplied in this country is standarised stength, most common around the world, but many years ago insulin would be issued in different strengths.. There is 500u/ml, put this is only available in Amercia, and can only be imported into this country by a consultant for a named patient...
And basically the dosage that they've got marked up, because with pen or syringe the mimium that can be inject (that is if you can get hold of a cable pen or syringe) is 0.5 unit... The only piece of equipment that I know that could deliver such a small amount of insulin is a insulin pump, and this is used with quick acting insulin only... Not lantus or other slow acting insulins..
I ponder what amount was injected, as it's impossible to inject such a small amount in the first place, and if you could inject such a small amount then it would very unlikely cause your dads hypo (low sugar levels) I think you need to ask them if they can remember how much they might have injected and when.. Lantus is a timed injection, it is normally injected once a day, at a set time, i.e every night at 8pm, if it's given twice a day then you would inject at 8am and then at 8pm...
I would suggest if you haven't done so, is make a offical complaint... But first get hold of the diabetic clinic or dad consultant team, and demand that his injections, dose to be use and the ins and out's is sorted now, so that not only your dad but your mum knows what to do and what to expect...
It's seems that a serious error has happened here, by discharging your dad from hospital, with out ensuring he or his carer (mum) has been given the correct information for the treatment of his medication regime...