past_the_moon that wheel direction test isn't 100% reliable. Professional diff builder told me that. good luck.
Lets settle for 95% then. The Volvo Dana (Spicer) LSD centre is 100% mechanical and contains two sets of wet clutch packs. That’s one for each axle, that acts as a firm preloaded so to speak.
So when placed on hoist both wheels will rotate in the same direction.
However, if the LSD is worn out bad, perhaps there is not enough preload anymore, or has internal serious damage with munched parts, or externally a seized wheel bearing or a dragging brake disc, then this could add up to 5% uncertainty.
Nearly all LSDs should have a tag or sticker or something to indicate to the mechanic that special LSD oil is required (extreme pressure type with no friction modifiers).
Anthony