Despite the prevalence of virtually most Lambrettas now converted to electronic ignition, a properly serviced OEM ignition is likely to contain superior components, despite the age. Definitely more reliable than many Indian set ups. You only have to read Forums like this to see that.....
Mechanically, removal of any coil involves desoldering the relevant connections, easing over the laminates retaining the coils using a metal spatula (no point in damaging them!) & easing off.
Inspection of everything & thorough cleaning then replacement of any affected coils/re-wiring will result in a fully functioning stator.
There are probably guides but I can't be arsed to look right now. Either on here, Scooterotica or SLUK & you should really consider changing to 12 v points ignition. Even I have managed to do so with components from 50+ year old parts that looked brand spanking new once cleaned up! Unlike the Indian stators that arrive 'pre-distressed' (Am I getting my point across ?

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Despite his thriving business selling reliable electronic ignitions, I seem to recall Anthony Tambs will have done guides for those of us that cling to the reliability of OEM ignitions.