Hi Deb
There are loads of alternatives to the 2 Ls! Like Copepod, I'm amazed that everyone seems to be put on analogues at diagnosis these days. The reason for it is pressure/financial incentives from pharmaceutical companies, and partly ignorance of medical professionals. Here's a page from this website that lists alternative insulins.
http://www.diabetes.co.uk/insulin-in-the-uk.html
You could print it and take it to your daughter's diabetes team, but I'm doubtful they will have any knowledge of other insulins, and might even suggest they are old-fashioned, not as effective, or have been discontinued. While many synthetic "human" insulins have been discontinued, the older insulins and animal insulins work better for many people, especially those who've suffered problems on the newer analogues.
The reason Lantus is causing your daughter so much pain is because it is very acidic on injection, it then neutralises which is how it releases itself slowly. Lantus is the only medication that works in this way, she's unlikely to experience this with other insulin treatments. For some people Lantus can cause unexpected and unexplained hypos, I experienced this, but as Copepod stated it is more likely the mismatch of her rapid-acting and carbohydrate. It's very early days yet, and hypos are unfortunately likely at this point, learning to carb-count will be very beneficial.
Everyone is different, it will take time to find the best insulin and regime for your daughter. If you have any concerns you should expect your daughter's team to address them and work with you.
Jus