Abraham Kawaii lomi lomi is commonly called temple style lomi lomi for people trying to differentiate what type of lomi lomi it is. If there is 'flying' (the name of the dancelike feet & arms moves required to get the famous flow of the massage going), it's temple style, if they have Abraham Kawaii in the lineage, it's temple style. If they have Auntie Margaret, it's not temple style.
There are other styles too. Celtic KaHuna also teach Heartworks lomi lomi, which is similar in the flow to temple style, but it is done with the hands. (temple style uses a lot of forearm moves) Heartworks has the same minimal draping as temple style. Heartworks is actually a lot easier to learn, short weekend course, and it's less demanding physically than temple style. Temple style you can build up a lot of energy and fell very energised after giving a treatment, but it can be physically demanding, though people don't seem to feel it until it's a crashing burn out, doesn't seem to come on gradually. The crashing burn out is like the endorphin high of sport, people over do it (we're talking lots more than 20hr a week), and then it just crashes. Temple style was originally basically a rite of passage type treatment, just for special occasions, usually just for royalty/high ranking people, people would not be giving temple style often. It traditionally is a marathon style massage, it is meant to energise the practitioner, because it was often done for days on end, 24hr a day, with different people doing the treatments, until the shift to the next level had been made.