I've had two lambrettas. Sold my last one about 3 years ago. I had a 1966 silver special and then a 63 li 125. Both were bored out to 175 xx which was fast enough on 10 inch wheels. Both were registered as 125 s too. I actually never rode legally, once on false plates for about 2 years before I got it registered, the police tend to know fuck all about old scooters. The plate was off a vespa. As for reliability I can honestly say I never had a problem with either. Get it well serviced, all new cables and you shouldn't go wrong. You can pick one up around 3 grand and they are investments too.
I only ever had one vespa for a short time and I didn't like it anywhere near as a lammy. The balance thing is nonsense tho. The engine is on the side but the spare wheel opposite kind of counteracts that. If you go down the modern scooter route, someone has actually brought new lambrettas out, think they are called Ln s? I've seen one in a bike shop in shipley and it looked pretty good. Better than any other modern scooter anyway.
Lots of my mates had lambrettas and they never really had any issues either. The key is to change them to 12 v electronic ignition, get a fully stripped down and rebuilt engine with a kit on. The imola 185 kit is a belter. Very reliable and fast as fuck.
Get around better, get a lambretta