You really need to know what pressure you have normally, then decide what to do about the periods of low or no pressure.
On the early V8's it's a gear pump and you can fit a new set of gears and shafts, and if the end cover if machined/ground flat then that will almost renew the pump.
One the later engines it's a Hoborn-Eaton rotor pump and comes with the front timing cover as an assembly, for a LOT of money. Rotor sets are available on ebay but not from Land Rover, who only sell the timing cover assembly.
Relief valves could also do with cleaning and maybe reseating on the early engines, I don't think that the later ones are easily accessible.
If the oil pump pickup is exposed when running at high angles then you'll lose oil pressure when driving, not a good thing. Later V8's had the modified sump in alloy which concentrated the oil reservoir into one smaller/deeper area and the pickup tube was modified.
Peter