The IGH needs two different types of lube. First, it needs some sort of gear lube for the whole assembly. Many people have had good luck with ATF (automatic transmission fluid), including me. You can buy the expensive shimano stuff if you'd like. I don't think it's necessary.

Then you need to grease the bearings, and that's just whatever grease you usually use for bearings. I bought the park stuff (green) a while ago and just use that for most stuff, however I think I got the shimano grease when I bought the hub, so I just used that for the hub bearings.