Hypoglycemia can be a problem with or without medication so it certainly bears watching. With diabetes we're conditioned to worry about high or artificially low BG but naturally low BGs are concerning as well.

Have you tried testing with another meter to rule out technical issues?

Do your BGs run low now (or at the low end of normal) all the time, or are these pronounced dips? If you just tend to run low in general that would concern me less than if they are normal most of the time, but very low occasionally.

Are there behaviors that go along with the lower readings? For instance, are you eating later or less (or more) the night before, or getting up earlier than usual?

If you aren't having any symptoms and your BGs are normally fairly low I would probably eat something LC (not "treat" the low with fast-acting carbs, just have breakfast) and make sure it does eventually wander into a better range. (For example, my fasting today was 63, which is lower than normal for me but not unheard of. I feel fine and I know that I got up earlier than usual so I'm just eating an omelet and will retest in an hour.)

But if these are dips you don't normally experience or you do start having symptoms I would definitely investigate further.

Either way, be sure to study up on how to treat a low with fast-acting carbs and keep some around, just in case. It won't hurt to be prepared.

Congrats on your success so far!