Hi, I used to have the same problem with lantus, although at a different time. I'd have good bloods when waking then increase until 2pm roughly. Basically blood sugars increase throughout the day normally and the lantus should control this, but sometimes blood sugars might increase more at particular times of the day than others and the lantus might not be able to cope with this. Turns out my lantus took ages to start working and didn't work properly at all.
I'm now on an insulin pump, which is attached via a cannula, so I have insulin infusing into me all day. Instead on just one injection of my basal insulin (lantus), I have a small amount of insulin infusing into me all day, every hour. I can set different basal rates throughout the day to cope with highs and lows, e.g I need 0.9 of a unit every hour between 8am and 12noon as my bloods are higher during this part of the day, whereas between 4am and 8am I only need 0.5 of a unit per hour as my bloods are not that high. Its fantastic. I can set different bolus rates, blood glucose targets, sensitivity for corrections, and I can set temporary basal rates for exercise etc... Love it.
Good luck with your lantus, hope it goes well.