As Shanny has suggested, try moving your Lantus injection to a bedtime regimen. There's a possibility that your Lantus isn't working the full 24 hours. Let's say you get up around 8 AM, you get dressed and then go take your FBG and then do a dose of Lantus. If your basal insulin isn't covering the full 24 hours, which has been reported in some diabetics on Lantus, you may find the 8 AM test not proportional to your normal BG throughout the rest of the day.
If your Lantus runs out at say 20 hours (4 AM) then coupled with a DP a meter reading of 160mg/dL is quite the possibility. Try this in order to find out when your Lantus may be used up: Change your injection time tomorrow by waiting until 2 PM. Do this for 2 days until your system gets used to this. Ignore your FBG numbers for 2 days. On the 3rd day stay fasted, start taking blood tests at 8 AM, 18 hours after your day-before 2 PM injection. Test your BG every hour on the hour until 2 PM. If your Lantus is waning off before its 24-hour period you should see some rise in your testing numbers between 8 AM and 2 PM.
If you DO find that Lantus wanes off too early you do have choices. You can do the Lantus at night which may lower your DP...but still doesn't cover the few hours of its waning period.You can split (stack) your dosage so that you do X amount of insulin at 8 AM and another X amount of insulin later that night. It's a (sometimes) recommended regimen for Lantus...but mathematically that procedure still leaves you with a cut stacking 2 hours before each injection, instead of 4 hours before a full injection. Then there's the Levimir camp that finds their insulin works better in multiple doses.
Myself, I started out with a bedtime script for Lantus. Got night sweats...got tired of doing laundry once a week, went to a morning injection. My FBG numbers went up from 95 to 105-115, but the sweats stopped. Since FBG numbers don't last once you rise...I chalked it up as a good trade-off. I tried increasing my morning basal dosage to try and change the FBG numbers the next morning...that was a mistake. I'm now of the philosophy that injecting even one more unit of insulin than you actually need...is a BAD idea.
I also noticed that snacks, or your "4th meal" after sundown affects you FBG. I had to go in for labs yesterday morning so that required a fast - skipping my 4th meal of the day, usually around 8 PM. Normally, my FBG would be 110. Yesterday morning, after fasting for 12 hours and no 4th meal the night before, it was 95.
Whatever changes you decide to make, or not make, please...keep us posted. It's good information for everyone here.
FWIW