What is the intended connotation of addressing somebody by 'lovely' in a letter or an email?

In the first case she could mean "thank you that would be lovely" if you'd offered to do something for her. It would be ambiguous so you shouldn't read too much into it.

Otherwise, English is very variable. In many areas of Britain, terms of endearment are used towards complete strangers, which would sound very strange out of context. To further confuse the issue, not only does the use vary with place, but it's changing with time as well.

Then you have to consider other national varieties of English. I have seen "dearest" used in Indian English in cases that seem strange to British people, for example.

So to get to the bottom of this, you'd need to consider not just her language, not just her country, but the region of her country.