I was at Lady Musgrave for a few days (May 2006) when I was relatively new to kiting. Had 4 days there and occasionally the SE dropped below 20 knots...but not for long. I haven't been to Lady Elliot.
www.seabreeze.com.au/gallery/gallery.asp?imageid=1814Given my lack of experience I did relatively little kiting there. With a big(gish) sea the swell comes over the fringe reef at high tide and makes the lagoon quite lumpy. The tender we had was very small - so getting to the island at high tide was not an option (we nearly sank on our first try). At low tide, the reefs immediately around the island are exposed - so launching is a real problem.
If I had the chance to go now and had a reasonable chase boat, I'd certainly take it. I think you'd have to be able to drift launch - kites and coral beaches really don't go well together. The one time I did go out I pumped up with the kite in the tinnie in the shallows...not very convenient. I'm sure there are plenty of pointers somewhere here on Seabreeze about boat launching and retrieval. If you were camped on the island, I guess it would be doable - though I think you'd want to have a sewing machine and repair gear with you. Staying on a boat in the lagoon, with the difficulties of getting to the island, made it a tad difficult. But, as I say, with a chase boat in case of gear failure or other emergency, kiting the lagoon would be spectacular.
Not sure about the comments about off shore breezes. It's an island...so go to the beach where the breeze is on shore (with some cross). Although it's quite small, it's quite big enough to give you enough safety for quite satisfying long tacks. Certainly if you were out in the lagoon, you'd have breezes taking you off shore...hence the chase boat suggestion.