The Schaublin 13 lubrication pump deserves a service now that there is no oil in circuit and it is easy to disassemble.
Given its simple design, to service it you should just replace three or-rings. Two of them are the seals of the pumb body, that avoid oil leaking from the tank. The most interesting to replace, however, is the o-ring of the piston. To replace it you should first free the piston by pushing a pin out. This can be done by aligning a specific hole on the piston: this allows to reach the pin with a pin punch drive. The following pictures show this process. The right sizes of the three o-rings are tabulated in the blog entry about o-rings.
The next picture shows the hole used to push the piston retaining pin.
After aligning the piston pass through hole, you can push the retaining pin.
This is an exploded viwe of the pump piston and one of two ball valves inside.