A good jack mif it will work satisfactorily. Lake and alliot were a good marque.
When I needed seals for a bottle jack (Being used in a bench press) I got some from a local seal supplier.
In my area, I would try Anglia Bearing Co, so look for a similar supplier near to you .
When you slacken the big top nut, whatever oil is present inn the jack is going tom pur out from around the base, so have it on a tray with plenty of rag ready!
Ideally refill with a hydraulic oil (Tellus? ) to your local oil company depot for their recommendation.
If the worst comes to the worst just use ordinary engine oil. The flow rate is minimal, and all that is neded is for the fluid to be incompressible.
It could be argued that the higher the viscosity the less it is liable to leak. But conbversely, thicker oil will make the jack harder to pounp up, and slower to retract.
HTH
Howard