Hi there
the basal insulin (ie the lantus) is intended to cover the gentle drip-drip of sugar into the blood from your liver, where it is stored. If you had a day where you ate no carbs at all, and your basal is at the right level, your blood sugar should stay pretty much steady. If you can be bothered to do it, a carb-free day to check this can be a useful thing to do.
However, you may find as time goes by that your background/basal insulin requirements change... you may get fitter (and need less insulin) or less fit (and need more insulin), you may find that you need more insulin as you get older, all sorts of things. So, for example, you might find you are getting hypo in the night, or you find you are waking up with high blood sugars, or you are getting hypo late afternoon even though your short-acting insulin has run out... stuff like that. And in those cases you might adjust your basal.
I personally would only adjust basal 1 unit at a time, and leave it a few days (I would say 2-3, others might say longer) before adjusting again. If you are happy adjusting your short acting doses, it's the same principle really with long-acting. Tweak it and test, until you are content.
In my experience, I think I started out on 12 units basal many years ago, my top whack was 18, and I'm currently on 16. So it does change over time.
PS some people take 2 injections of basal insulin, splitting the dose morning and evening, because they find it more flexible and/or because their basal doesn't last the full 24 hours. I have not covered this because I don't have personal experience of it, but someone will no doubt be along to say more on this from their own experience.