This is a very simple form of doing a static balance and is a good start to getting it better than not balanced at all.
With what is called X,Y & Z axis these are terminology used in the machine shops for milling and machining.
These are;
Forward and Back
Left and Right
Up and Down
So I'm not sure how any other axis can come into play here other than the rotational direction on the vertical plane. It should not move left or right nor up and down.
So doing this simple test and correction using stick on wheel weights is the safest way to go because drilling out excess metal is a final one way journey for balancing and only recommended to be done by experts in balancing engines etc.

To check the injectors they need to be removed. Then you can reconnect them to the fuel line and wind the engine over and watch the fuel spray. It must be a very fine spray. DO NOT put ypur hands in front of the spray as it can piece the skin and make you very unwell.
As for other possible causes you would need to check tension on the flywheel bolts. Are your filters clean because if it is starving for fuel or air this can upset the apple cart. Is there anything hanging off the prop underwater or a piece mising off it? Is there a bend in the prop shaft.

I look at it like this and that is everyone is entitled to their views, we dont have to always like them but it is they way life is. It would be very boring if we were all the same.
Sometimes I didn't agree with statements made by posters, so I either stopped reading that post or thread and went onto the next. I didn't take it to heart.

Hi Tedly. Just saw your reply from that old thread and now here. There is a bloke from the New England district that has Lister parts out here and I know that he is heading to the Allora Rally this weekend. SO he wont be able to be contacted for a few days. His name and contact details escape me now but there was mention of him on Smokstak or TOMM and is how I know where he will be.
Usually these things are very basic and simple to work out how to repair. What I do is set up a large area that is clean and a big rag or towl to work over and start taking it apart one piece at a time and taking pics with the phone at every step paying attention to what way they came out. You may find that one of the ball bearings is pitted or the seat for it needs a touch up or even a broken spring inside if there is one there.
My last restoration had me scratching about with an oil primer that was incomplete. Once I got another one it was seized so I zapped it in the electrolysis tank and looked at the parts inside. IT was so basic I did not understand why it worked. One thing that stood out was the ball bearing and little spring. Off to Bunnings to buy a spring of the siame OD and gauge then used side cutters to cut it to length. Ball bearing was in good condition so out of habbit I put the baody of the pump in the vice with a block of wood under it and got a pin punch and put the ball in place and hit the punch. This reforms the seat and now it pumps so well.
So you can become adventurous and take your time and it will work out.
Try doing a Google search for your model engine looking for a manual, sometimes they do turn up.

Do they run? For that price they would need to be a runner. If they don't run you are paying big money for scrap metal. You can also copy and paste the name and use google to trnslate the name of it to establish what it is.

X2 to what BruceM said.

G'Day Mike,
Thank you for the suggestions.
It has ran beautifully in the past with tttthis full flow oil filter on it from a VW with no problems with restrictions.
I will have a look for a splash dipper next time I can get to it as we are having a wet spell here at the moment and will also check for frothing of the oil but have not noticed it in the past but does need to be confirmed.
You mentioned a blockage. Thoil when under pressure goes in one side at the crankshaft bearing then across to the opposite side then up to the gauge and this is where I took the pressure reading from so I am guessing there is  no blockage unless there is another line or gallery I dont know of.

It is a true mystery at the moment and I need to get it sorted. SO next chnce I get it will be more investigating.

Hi,
I have owned this engine for a few years now and due to other projects it has been left alone under a tarpaulin to keep the weather off it. This is a 'high speed, tropical' model which runs a dry dry sump set up and is why there is the extra filter and oil tank on the back of the engine. Before leaving it alone under cover this engine always started and ran very well. Now I have an issue with it seizing up after running for a very short time. This is out of character and I need to fix the problem. There is plenty of oil in the tank and I do turn the oil tap on before starting and there is oil pressure showing on the original gauge but it is knocked around so I connected another gauge and it shows good pressure of around the 15psi as specified.
When I start it up it takes maybe 3 full swings on the crank handle then use the compression lever and pull it down or push it up , it doesn't matter and it starts. I run it at just above an idle speed and possibly after a minute or so it starts to slow down so I decompress it and shut the fuel off as well.
After this happens I cannot swing the engine over with the crank handle but I can use a pair of stillsons to wind it backwards. Once I have done this I can swing it over on the crank as if nothing has happened.

Any clues as to what to look for please as I miss hearing this run and it is a soothing sound with no muffler just ticking over, even at half revs. Any help is greatly appreciated so than ks in advance.