Not recognising hypos!

I am a little concerned that I'm not recognising the signs of a hypo like I used to. My pre-breakfast reading today for instance was 5.9. That was at 8.00. My insulin was half a unit over what should have matched carbs.(the current pens I have don't measure in half units...something I shall ask for when I need replacements). I have had a succession of phone calls and although I felt really hungry when I finally tested, I had no other symptoms. My reading had shot up to 12.2.so I can only assume that I went low and then my liver dumped glucose instead. Is that correct? At what point does the liver do that or is that just something that can happen at night? I thought I'd keel over if reading went too low or does the liver always help out?
Besides worrying about not recognising hypo coming on, I'd like to know, does it harm the body if you get into a pattern of the liver dumping glucose without you realising? sorry to ask so many questions. I just know I'll get a clear, informed answer on here.Thanks in advance for any advice.

Thanks for the replies. I did not explain that I didn't get the really high reading until 3 and a half hours after eating, so would have thought Novorapid would have worked long before then. I know before I split the Lantus I was being woken up bathed in sweat and reading had gone high, which is why I queried if this can happen in daytime too.I don't drink alchohol at all, so thankfully, that does not come into the equation and I'm only on very small amounts of insulin, which is why I think the junior pen may suit me, when I can get some.
I just wondered why I had a high so late in the morning, when the amount of insulin was over what I needed.(All be it by a small amount.)

Thanks for the advice, Sally. Normally my readings for that time of day are in the "normal" range, so perhaps it was just a blip. If it happens again, I will definitey try adjusting the Lantus as you suggest. Thanks again.