Sorry for all the questions! We don't mean to be unhelpful, but there isn't necessarily a clear answer. It is obviously not desirable for her to be up in double figures for several hours of the night, but what happens when you do nothing? Does her BG remain high, or does it drop to normal range by wake up time? As I said above, when my son was on Lantus as a basal insulin, he crashed overnight and so had to be artificially high at midnight so as not to be hypo by morning. If I had injected some novo to bring him down in the early hours, I would have precipitated a hypo, so my hands were tied. If, however, the Lantus had acted as it is supposed to, and kept his BG steady overnight, I would have injected some novorapid for a high BG at 2am.
You may find it useful to give some novorapid with the bedtime snack if she ends up high at 2am more often than not. Two biscuits are around 20g carb (depending what type!) so quite a lot to have without insulin. I would also recommend doing some more frequent testing for a night or two (exhausting but worth it 🙂) - to have a picture of how the BGs are varying e.g. 8pm, 10pm, 12am, 2am, 4am. If she is perfectly fine 3 hours after her bedtime snack and it starts rising after that, you can narrow down the cause to either growth hormones or Lantus running out. Since you give her the Lantus in the morning, she may have inadequate basal by the early hours of the following day, and therefore a correction may work for you. But you will only know for sure by doing the intensive testing I'm afraid.
Finally, I would really recommend you look into getting an insulin pump for your daughter - the variability throughout the day is so much easier to tackle with a pump, as you can program different basal rates for each hour of the day to suit her varying needs. 🙂
Are you carb counting food? Do you give the same amount of Novorapid for each meal? Have you been taught how to give correction dose's of insulin when high? Do you know how much 1 unit of insulin brings BG down by?