Good morning phil,to the best of my knowledge Lloyds is a part of Northern Rock and Blackhorse Lenders. American express is a credit card but a different type from the ones offered through a bank, i.e, visa and mastercard.
Maybe recently, Lloyds and American Express may have merged to do an airmiles scheme. I do not know.
Here is a link that describes all the credit cards maybe there is an answer there.
http://www.uswitch.com.
I'll google again and see what I can find. Keep checking back here to read other's posters replies. One of them may be certain of any affiliation.
Hope this helped.
All I have left is my humour.