If you want reliability, you should read up all the problems associated with electronic systems before you buy into the hassle!
My advice is to keep contact breakers but modify the stator & rectifier to obtain 12v DC. Lambrettas that break down/run out of fuel etc still occurs & to be stranded on a busy road with no lights because the engine won't run is not my idea of fun. That may not be the reason that the conversion 'back' to batteries is occurring, but I cannot think of a better one.....
There are a number of web pages that will tell you how.
This one should work for you:
https://scooterlab.uk/convert-your-ac-i ... -workshop/This useful article was written by a guy that is very well respected & makes his living from supplying upgraded electronic components, yet he acknowledging that to some of us, there is a budget to be stuck to.
Welcome & Good Luck
