No, the MK3 LSD is of a different housing pattern. The LSD for any NA or TT automatic Supra will drop right in, however.
From companies based in Japan, any LSD made for a Supra built 5/96 or later will work, as later JDM TT's all had the same size diff.
Early JDM TT 6-spd cars and USDM/Export market TT 6-spd cars got a larger differential, which can be swapped into any Supra or SC with the correct axles and driveshaft, but the LSD and R&P sets do not interchange between the 'small' diff and the 'big' diff.