I believe you are right, Jorun, personally I usually refer to this particular plant as Phyla nodiflora.
I have a book, ABC of Flower Gardening in Cyprus, written by Lady Murphy and published in 1962 (actually this is the 2nd edition, I believe the original was published in 1956 but I haven't been able to track down a copy). In it her ladyship states, under the heading Lawns, that she has "....found the best substitute for grass is a creeping plant called 'Lippia', which thrives all through the hot weather if watered during summer, and it spreads rapidly". I'm sure this must be what we now call Phyla under one of its synonyms/pseudonyms? Just goes to show that the attempt to find a grass substitute is nothing new.