Possessive of a word that is already possessive

Solution 1:

I think you kind of answer your own question. If "Lord's" already is a possessive, then there's no need to turn it into a possessive even further. I would just say "Lord's customer services", much like I would say "McDonald's burgers" and "Ben & Jerry's ad slogan" and not "McDonald's's burgers" and "Ben & Jerry's's ad slogan".

Solution 2:

If you really need the genitive case (possessive), you could say: 'I was very impressed by the customer service of Lord's' or '. . . by the Lord's cricket ground's customer service'. You could also consider Lord's as an adjective describing customer service, which would make it '. . . by Lord's customer service'.

Solution 3:

I suppose if one is very concerned, one could contact them for advice on the matter. I looked at their web site and found that they use the following kinds of forms:

the Lord's Shop provides everything from unique Lord's souvenirs to cricket bats and equipment, ...

.. visit the Lord's Tavern Bar & Brasserie, ...

So it seems RegDwight's answer is correct.