The '81 ST had a 6.7" T series, non LSD diff.
No vehicle with a T series diff sold in N.America had an LSD.
Options are:
1. T series LSD used to be sold by TRD USA until about 5 years ago - find a second hand one but be prepared to pay for them in hen's teeth.
2. Hope for a second hand T series LSD from overseas (optional in Japan and standard in UK GT models) but get some more hen's teeth ready.
3. Swap in an MA46 or MA47 Supra (1979-1981) rear end. These used the stronger 7.5" F series diff and often had LSD from the factory. Even if it is not LSD, most 4WD shops have LSD F series diffs to suit the Hilux/Pickup which will fit the Supra housing.
4. Swap in an IRS setup from an MA61 Supra (1982-1985). Gives you IRS, LSD, F series diff and disc brakes but you need to cut off the panhard rod mount (point of no return) and **very** carefully drill in new holes for the Supra's K-frame.
5. Get a diff shop to custom make a Ford 9" diff. Might be able to use your old drums or possibly use something from Ford. Wheel lug pattern is 4x114.3" which I think matches some 1980's Mustangs.
Wish it were easier.
I got a disc brake rear end from a Japanese MA45 Supra with a T series LSD but that was definitely a one off lucky break.
http://members.iinet.net.au/~stepho/celprod.htm#cel43pr
http://members.iinet.net.au/~stepho/diff.htm#sets
- Stepho