Firstly congratulations on your huge A1c reduction! You should be very very very happy with that!
I know Lantus effects people in different ways. I never had any form of DP (low or high) with Lantus, and I am soon to move onto the pump - 6 days to go!
I would suggest a test at perhaps 3 or 4am each morning, and a pre-emptive bolus may be in order.
If this doesn't work, try moving your Lantus injection to the morning and see how it goes.