Lanai is part of the United States and under Hawaiian state law, he can't even close the island to outsiders (all beaches must be accessible to the public in Hawaii).
That said, he is the only true land owner there (Four Season's though must have some kind of long-term lease) and iirc, most of the ~2K people who live there don't have any kind of long-term leases and can be evicted. Of course, to maintain an island that large, you do need people.
That is incorrect. He bought 98% of the island - the town of Lanai City is on the remaining 2% of the island. Aside from those who live at one of the resorts on island, the majority of Lanai's residents live in Lanai City and own their own property. Some of the families there have been in the same home for generations. I'm sure there are a few people on leasehold land who could now be evicted at any time by Ellison, but they could just have easily have been evicted by Castle & Cook previously.
I can imagine they're perfectly safe unless they start to make crazy amounts of money leveraging their space on Mr. Ellison's island in which case he'd either find a way to cut himself into the action or try to have them evicted.
That said, he is the only true land owner there (Four Season's though must have some kind of long-term lease) and iirc, most of the ~2K people who live there don't have any kind of long-term leases and can be evicted. Of course, to maintain an island that large, you do need people.