Has the daughter done connections on her own anywhere previously or even traveled by herself on nonstop flights? Has she connected at LHR very much with adults or other kids?

I consider LHR to be one of the more difficult airports for connections. Still, any reasonably intelligent adult or teen who can read and who speaks English should be fine, assuming that the connection allows sufficient time. I wouldn't advise anyone to try one that barely statisfies MCT unless the person is very familiar with LHR and the terminals that are involved.

I'm assuming that she'll have a phone, internet, and some sort of a credit card for emergencies as well as some money (in the relevant currencies along the way)for snacks and reading material or other small entertainment purchases along the way.

Note also the document requirements, including possibly a notarized parental letter granting permission for the travel.