Hi Ovi,
Sorry I don't have an answer for you, but I hope you don't mind if I piggy-back on this thread, as I am in a very similar boat.
I was also on Lantus for many years, and switched to Levemir a few months ago, and am still struggling with sugars rising from around 4/5am so I wake up high. (monitoring with the Libre)
I've always battled a bit with dawn phenomenon, but when I was on Lantus, I had managed to get it fairly under control - it would only start rising quite sharply after around 7 hours of sleep, and if I injected as soon as I woke it didn't peak too high. I was splitting my Lantus into 2 equal doses at 12 hour intervals (usually 8am/8pm).
Now on Levemir, I'm not sure it is actually dawn phenomenon, as it is an earlier and steadier rise. I've also been experimenting with the timing - pushing the evening one later and the morning one earlier (around 930pm/8am), but don't seem to have nailed it yet. So far I'm still keeping both doses equal. I tend to drop a bit for the first half of the night, so don't think I could up the night-time dose much, unless I also had some slow acting carbs as a snack before bed.
I usually eat dinner around 8pm and sleep around midnight. Currently on a medium carb diet. I have done stretches of low-carb in the past (when still on Lantus), and it did seem to help with the morning rise (I guess just less glycogen there to release).