I also have an 83 L-type with 5 Speed tranny and it came with an LSD from the factory.
Mods include:
K&N filter in drilled airbox, intake resonator replaced with straight 3" pipe, AFM loosened 3 notches.
NGK plugs (one step colder), timing advanced to 14 degrees.
Brullen 2.25 inch mandrel bent stainless steel catback exhaust.
Eibachs/Tokicos at all 4 corners.
Brembo rotors and KVR carbon fiber brake pads at all 4 corners.
Fog lights rewired to come on with ignition.
Weight reduction: All A/C components removed from under the hood (40 lbs), spare out of the back (40 lbs) plus a few other odds and ends.
LJM front strut tower bar.
Custom made rear shock tower bar.
CT-26 Turbocharger will be added this summer. I'll be needing some new tires soon! ;-)