I am a runner too, I had a difficult time dealing with my basal insulin, ( lantus for you Ultralente for me back then.
The trouble is that when we run our insulin resistance is reduced and our need for insulin is reduced as well.
I am on a pump so I can reduce my basal insulin to only 30% of what I normally need.
and continue that for 2 hours after.
It is much more difficult to manage lantus this way because you can't reduce it for exercise,
The best way to do it is to bring some carb gel with you and learn how much you need to stay in the normal range. Maybe half a packet per 2 miles or so,
On days that you run you can reduce your lantus a bit too.
You look young and thin, I'm guessing your carb to insulin ratio is too low.
You can easily test it, Start in the morning with a stable sugar, say 100.
Consume fast carb of say 30 carbs, Juice or something sweet works best.
Then wait 30 min and see the result. You will be able to see how 30 g of carb will raise your sugar, Then you will be better able to correct it ahead of time,
Then take the appropriate amount of insulin, for you it would be 3 units for 30 carbs which sounds like a lot to me. After about an hour more you sugar should be where you started if the carb ratio is correct. If you end up low, then you should change to maybe 12 to 1 or 15 to 1.
You need to start out stable and use a fast acting sugar, If you eat a meal the sugars will late longer to metabolize.
I have calculated my ratio to be 16carbs to 1 unit, On days that I run( about 7 miles) I change my ratio to 20 carbs to 1 unit.
When I was taking my injections I split my dose, I took half in the morning and half at night, It gave me better flexibility,
It will take a while to find your exact ratios.
It is also likely that you are going low at night and your liver dumps sugar to compensate and you end up high. It would appear you did not bolus enough, but it is just as likely to be you bolused too much.
If you could get a CGM you could see it more clearly. Either that or test more often,