There's no cheap or easy LSD solution for the W124. Yes it can be done, but expect the cost to be between $1k-$2k. Someone on this forum who's an MB tech can convert your diff into an LSD for about $1200, that was mentioned in a different post a year or two ago.
A possible option is to use the 2.87 diff from a 1995 E300 diesel with ASD, which has LSD internals in addition to the hydraulic locking setup. You'd need to swap the rear cover, and either the axle flanges, or use the axles from the E300 also. Otherwise, it should bolt up. Potomac German has a few available for $300. One catch... the LSD internals are usually toast after 100kmi, so it would probably need to be rebuilt with new friction discs. Figure another $200-$300 in parts if you do the work yourself, several hundred more if you pay a shop to do the work.
BTW - the 1986 300E has a 3.07 axle ratio. The 190E-16 has a 3.27 LSD, but would need the axle flanges and rear cover swapped, along with new friction di$k$.
More diff info:
http://www.w124performance.com/docs/mb/other/differentials.pdf
