"Reef Safe.....with Caution" is the operative term for a lot of fish. Some triggers fall into this category. Niger Triggers are known to be a little less aggressive in a reef environment (Genus Odonus). It may in fact be safe with a reef lobster....but unlikely. Keeping it fed (like any trigger) will keep it from wandering for live morsels of food. Starting with a small one with tankmates helps as well.
Corollary; Triggers of the Genus Xanthichthys: (ie. Blue Throat, CrossHatch, Sargassum, Kiri/Greenei) are more so docile in a reef environment. In the wild...they are planktonic feeders. I would venture to say more hobbyists have had success with these triggers with invertebrates that Nigers.
In my own display - I've had Blue Throats and Sargassums with cleaner shrimp, blood shrimp, pistol shrimp, and even peppermint shrimp.
Triggers in general are very animated and curious....which is part of their attraction to hobbyists. Curiosity has its downfalls too. Don't be surprised if these triggers one day try a shrimp or other invert. Mine like to pick on a snail now and then (probably to wear down their teeth). I'm more than happy to sacrifice a snail or the odd other invert to keep them around.
Fortunately; in my case - they haven't touched LPS or SPS that I have. You may want to avoid putting in freshly 'cut' or fragged pieces of any coral into your display with these fish or any other "Reef Safe with Caution" ones. Freshly cut/fragged pieces tend to give off a scent that may be inviting and peak their curiosity.
As always....keep them well fed...to curb their stomachs
Hope this helps. Good luck.