If there is a routine of being high in the morning, then lower in the afternoon and increasing again in the evening..
I ponder if mum is suffering from dawn phanonomon (sp) and with Lantus not lasting a full 24 hours?
It might be that you need to be looking at splitting her Lantus so that the night jab covers her needs durning the night and into the morning, and then a morning jab that covers her the rest of the day...
This would mean that more Lantus could be given to cover the DP and morning needs, and then Less to cover the rest when she needs Less background this would also enable the Lantus to cover the 24 hours...
If you decide that a split might be a good idea to try, then start with a even split of her normal dose, give her the first split dose at her normal time in the evening, and then her next split dose about a 12 hours later.. Monitor her levels closely so that you can see which injection needs adjusting, this can be dose or sometimes even moving the actually timing can help to solve problems.