I don't know if we have ever re-keyed a 124 door lock cylinder, but I imagine we have. The door handles and probably the separate tumbler section on 124 style handles, comes apart. it is not in the MB manual as there are no sub components available.
The way to fix these problems it to disaasemble the tumbler body and file down the worn tumblers (or remove them - there are plenty) untill the key makes them flush. When disassembled the needs will be obvious.
Bosch Master, ASE Master, L1
33 years MB technician