Fit a new lock nut and tension it up.
Yup, but there are some tricks to that. Hand tightening isn't sufficient; if you don't have a power impact wrench available, there is an alternative, that we used before these were widespread:
In the absence of a rattle gun, another way that nearly always works, is to use a long 1" AF ring spanner. 'Angled' type is better than 'cranked', but both will work.
With the mower turned on its side, use the toe of your boot to hold the spanner on the nut. Hold the blade disc edge tightly with one hand [gloves help], and hit the spanner hard with a steel hammer. About a 32oz ball peen hammer usually works best.