granny. you are correct.....lignocaine is a local anaesthetic and depending upon the dose should relieve the pain instantly for perhaps a period of 2 hours so that the patient may well get the joint moving again.
It is often given in association with a corticosteroid which takes longer to act.
So.....when the lignocaine wears off. the steroid takes over.
Lignocaine can be given without a steroid, if there is just one painful localised area, so your son in law could have had either method.