If you take off the pipes, oil SHOULDN'T run out, more than a drip, but it surely will.
Once you have the pipes off remove from the machine.
If the outlets keep leaking after you remove the pipes, put them back, unbolt from the machine, put a tray underneath and remove the pipes.
If there is no continuous leakage from the pipes, then no probably is no need to remove from the machine.
The pipe on each side has it own respective spring loaded ball.
The idea is, that one the pump has pushed out some oil, oil can not run back into the pump.
There is a third ball valve that oil into the piston on the return stroke.
Remove it, fiddle with it with some oil. You will soon figure out what it should do.
Not rocket science, but the ball seat should have been at least good enough to seal from the spring pushing on the ball.
I removed the seats and forced a ball into the seats to form them properly.
If I remember correctly it is all removed from the bottom where the lever is, so empty it first or expect a bit of a mess.
Also, once all the pipes are filled, and the spring loaded balls seal the start of the tubes, no oil can leak out the machine end,
unless other joints in the system leak, and air can get in.
Any leak will allow air in, and some small leakage will occur until the tube drains.
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.