Both your Lantus doses are independent, so what you need overnight wont have any bearing on the day....you should also try and only change one thing at a time.....
from the last few days I would say the 6 units of Lantus at night is pretty much there, so it can be ticked off as correct for now.....you can now focus on the day time....
Because you went low in to the afternoon that could suggest too much basal [provided it wasn't any previous bolus/bad carb calculation etc] but its too early to tell, more testing required unfortunately....
So 14 units the next morning [is it morning for you now....?] and test away...
Should you eat a carb, yeah, you can........having a small carb as early as you can alongside some insulin will actually help the DP process come to an end....and probably more effectively than a carb free breakfast, due to the quicker digestion response...
[READING BACK: I sometimes get carried away with dosing advice. I am not a doctor, just an experienced diabetic, so take this advice with the normal caution you would take when making insulin adjustments....
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