,,,,
Seems the Omega A / Carlton LSD is slightly easier to find but was a solid-mounted diff. People say that you can just swap the inside LSD part but there is little info
Omega A / Carlton
and senator B internals ,possibly the Brazil built Chevrolet Omega (1992 and 1998)

Australian Holden Commodore

Back when I had Carltons ,IIRC , people where using Omega B internals for Carltons (because they where cheaper/available )
swapping the internals ,IF you can find them

would require being "set up" correctly ,
Finding a WORKING LSD made 1986-1998 might be difficult

GM LSDs of that era need to be used and serviced and don't like being stored as i understand it.
Surely with all the high powerd Omega knocking around and those in the eastern countries with Snow and ice there must be viable LSD options or are people swapping in something else ?
Omegas where comfortable ,mile munching ,cruisers, NOT race cars or drift machines
to use an Omega for race or drift requires major expensive upgrades
so.... IF that is your intension

, you probably will have to spend serious money
there are much better suited cars to race and drift .
If you just want an LSD for snow and ice etc , spending money on decent tyres would be a better use of funds
though I suspect you don't want rear wheel grip
