Hi Alex,
Fishing at Lord Howe can be quite exceptional, but there are a few things to be aware of.
There are pretty tight weight restrictions on the Dash 8 getting over there. 14 kgs and they enforce it, so forget the idea of taking a few dozen 500gm jigs with you! You do need to be fairly discriminating with what you take. If it is an issue you may be looking at some of your baggage arriving a day or so after you, which is not the end of the world anyway.
Also, fishing on LHI can be (is!) very weather dependant and the wind dictates. This can have a big impact on whether the boats can get out or not. When land based fishing though, there will always be a protected area where you can get a line in the water. Some areas are now marine sanctuaries, but there are still plenty of spots to go, although you may have to walk a ways.
Now, having got the the warnings out of the way, what to do? If you are wanting to get out beyond the lagoon and chase the fabled LHI kings there are a number of operators who can help you.The two that I have used extensively are Jack Shick (Noctiluca)and Dave Gardener (Greenback). These guys are serious about their fishing and it is their primary business. As a result they are way more likely to want to go fishing than a few of the other operators who, how do I put it? - operate a bit more on island time and have other things to do?
They, and most of the other operators, are more focused on jigging, live baiting, trolling and bait fishing than popper fishing, but that doesn't preclude you from popper fishing. I have found that better results came from using sinking stickbaits, as poppers tended to get mobbed by the smaller rat kings that seemed to be more active around the surface. The deeper I fished the bigger the kings. I'm more of a popper fisherman than anything else, but Lord Howe really lends it self to jigging.
Another thing to be aware of is that there is not a lot of catch-and-release at Lord Howe. The boat will keep all legal sized fish and they are used to supply the island with food.
I've done a fair bit of land based fishing off the rocks at LHI and probably lost more tackle there than anywhere else! There are brutal ledges that undercut the shore and it can be a challenge to keep fish out of those areas.
The person who can no doubt give you a lot of good advice on fishing the rocks at LHI would be our forum sponsor, Duncan, who has spent quite some time on the island and can really speak from experience.
It's a fantastic place to spend some time, the waters are stunning and the fishing can be outrageous. You just need the wind gods to be on your side.