First thing, WAY above everything else…“No snacks!” Wait…what? Don’t tell me when and what I can eat. I don’t care WHO you are.
I understand that it’s your habit from trying to prevent a low overnight, but you have a Dexcom.
You can watch your trend before you go to bed and eat and/or bolus accordingly.
BUT, if you enjoy a bedtime snack, then have one! I know I hate to go to bed hungry.
Hi Jan 
I use Lantus as well, but I split my dose into 2 shots. I tend to generally need more insulin in the evenings and less in the early morning hours, so I time my Lantus doses accordingly.
I take one shot at 9 AM and one at 4 PM which means I have the most insulin on board in the late evenings and the least in the hours just before my morning dose. I split it around 50/50, but sometimes my morning dose is one unit higher. I routinely vary my dose based on my hormone cycle. I also make some non-routine adjustments for planned extra activity.
Regarding your question about target range, the simple answer is that my target range is 70-120 during the night. My ideal scenario would be to hover in the 80s all night. Most of the time I tend to get a small rise in the earlier part of the night that either levels off or turns into a small downward trend through the rest of the night. When my insulin dose is spot on then I am flat all night, but minimal slopes don’t necessarily warrant dose adjustments. My dose varies by 4 units depending on the time of the month, and I adjust my morning and evening doses based on the slope in the beginning of the night (indicating a need for morning dose adjustments) or early morning (late afternoon dose adjustments).
If you’re giving your Lantus shot at night, then the upward rise may be due to not enough basal insulin in your system and the downward trend in the early morning may be your Lantus dose being at full force. That may actually indicate that your basal dose is overall too high- except for that brief period of time where your last dose is wearing off and your current dose hasn’t fully ramped up yet. It could also just be that your body needs more or less insulin at certain times of the night.
If your bg is already rising slightly between 12-3 AM, then it is surprising that you’re dropping low before or around the time you wake up because that means you have that much further to fall. I would be inclined to think that this is a problem with doing only 1 Lantus shot a day, but I may be biased.
OMG!!! my former idiot endo used to do this. it was so confusing that I became afraid to eat anything that wasn’t in my “safe” category (which provided me with consistently perfect BGs) then I came onto FUD, and my entire life expanded. I got a new (young and good looking 
) endo, , and he’s totally the coolest in the world. He says things like “eat whatever you want,” “experiment” “enjoy yourself” “no worries; its all a learning experience” “I can’t tell you what to expect bc everyone is different.”
wow, what a relief. a new freedom passed over me and I am a changed person bc of it.
and all bc of FUD’s purpose: Living life without limitations!!!
DM