Paula,
I often "dip" before a meal, when I was on lantis and in my case novorapid.
According to the books, it means that you are using the Lantius for your carb intake, as well as for your background. I tried lowering the lantus a bit, and upping the novorapid slightly.
I am sorry to say I never got it to work. As has been said, you need to monitor this over a couple of days/weeks even..just to make sure it is a pattern, and nothing to do with time of the month, the meal that you had that evening, the fact that you were particualry stressed, chilled out that morning.
For me, I went back to how it was, and had to be especially careful when it ws coming up to meal times. 5.3 is not low, and is something I love to see on my meter...but you do have to be careful if you were going to have a lie in etc.
I sorted it out by getting a pump in the end.
It is early days for you, adn you really sound to be doing well. In the honeymoon period, I guess it could be that when you woke up, your pancrease woke up abit, and produced a little insulin (Why am I thinking about Bagpuss after typing that!) It does take a while for thiing to settle down. You are doing the right things though..good luck!