I'm going to guess that it's a brake actuated limited slip, in that the computer applies brakes to the slipping wheel to shift power to the wheel with traction. That's how my tundra works anyway. If that's the case then an ARB should work without replacing the diff. Ih8mud will have the answer for sure.
ETA, heres your answer.. arb replaces the lsd carrier...
https://forum.ih8mud.com/threads/rear-diff-lock-on-lx470.48237/
This is not a limited sip. It is a version of traction control that uses the brakes to transfer power to the tire that is not spinning. 99 is the last year of the factory rear locker as an option. As he stated Ih8mud is the answer for all things Land Cruiser.
The Eaton that is mentioned above is an OEM locker for Ford and several others around the world. It is a solid product with no real issues.