It sounds very much like your mower has the 2-stroke PowerTorque Victa engine, from the description.
There are some free downloads in the numbered sections at the top of
THIS ODK page which cover that engine.
The wire that goes to the magneto is connected to one side of the ignition coil primary winding. An ohmmeter can't tell you much here, as the resistance of the primary is usually ~0.2-0.5 ohm. So measuring between that lead and chassis earth will tell you if the primary has gone open circuit, but that's about it.
With that wire detached from the carby, check the [coil secondary winding] resistance between it and the spark plug lead terminal; this should be in the region ~8.5-9.5k ohms.
Have you checked for spark across a spark plug, with that lead detached from the carby? The crude earthing setup is a frequent source of problems on these engines.