There shouldn't be any variance from year to year, The only thing that would be different is that Lister tended to use different springs and weights on the cam/governor depending on RPM, otherwise everything else should be consistent.
Having sat I would likely make sure the fuel pump and injector have not clogged or stuck. Otherwise just oil, filter changes, and maybe clean out the crankcase if it needs it. Also, see if it needs to be decoked which would require a couple of gaskets.
I don't know of any common issues with the HR series.
As far as parts to keep on hand, I would keep a couple of gasket sets, fuel pump and injector rebuild parts, and filters. One could go down the rabbit hole with bearings and bushings but would have to disassemble some of the engine to check if everyhting is still standard or weather the engine has had any reman work.
Where are you located? In Australia/NZ Oldtimerengines has a good selection of parts. In the UK stationaryengineparts has the same. There are a couple of places in the US as well.
Let us know how it goes, always fun to see another one brought back to life.
