To check the condition of the rings before dismantling the mower, remove the decompressor and replace it with a spark plug, then pull the starter a few times with the ignition off to see how the compression feels. Then remove the spark plug, put a spoonful of engine oil in through the plug hole, replace the plug but don't connect the lead, and pull it over a few more times to see if the compression has increased. If it has increased substantially, gas is getting past the rings. That usually means the rings are shot, though it could also mean the bore is badly scored. However it would be unusual to wreck the bore that badly without also wrecking the rings.
If the compression is good with or without oil in the cylinder, and the oil makes virtually no difference, the problem is not the rings, or any other source of blow-by. If that turns out to be the case, tell us and we can look for other problem areas.
