So you do see a pattern where you often rise during the night, an especially the last hours before taking your basal.
But you don't usually see nearly as dramatic a rise as today.
I would count today as a one off, can't adjust things based on a single odd diabetes day.
The sharp increase at around 5 looks like a pattern to me though, and you may well be on to something with your suspicion that your Lantus is running out at that time.
Many people found themselves more stable with taking their Lantus as a split dose morning and night. Or by taking their Lantus in the evening so they are awake when it starts to taper off and they can adjust the dose of quick acting insulin for their evening meal to cover the time their Lantus wears off.
I switched to Tresiba, which is longer acting and more stable for most, but it's also has the downside of not being easily adjusted for extra active days or sick days, it takes about 3 days for a dose change to take effect.
It can also be that you're not looking at the Lantus wearing off but at Dawn Phenomenon, or perhaps a bit of both at the same time.