No wonder people get confused..... my brain hurts
MOST lambretters run AC Lights
If it has a battery your headlight will also be AC but the horn and brake light are often supplied by the power off the battery. The tail light will still be AC and Bugger me it's the same bulb just 2 filaments. It even uses the same earth point, its all magic.
It may or may not have a regulator to help stabilise the output.
If it has a battery the AC regulator will normally have an EXTRA output to trickle charge the battery at wait for it....at DC.
The output at 12vDC is very low and not good enough to power anything like a rear brake light or horn by itself without a battery. Remember the bucket analogy, full bucket with a hole as long as the tap is filling it up more than is being used, it will not get empty soon.
A long time ago some one looked at the Greasers of the time with shit British bikes and looked at how good the light were. They had only slightly better stators but had battery's and often used Zennor diodes often fitted with large aluminium heat sinks coz they get ##### hot but basically had a similar set up to a car. Everything is running DC. The battery works like the bucket but most of the power supplied by the stator is going to the lights. What's left tops up the battery.
Those that have seen the light, opt for the modern equivalent of the Zennor diode.
With an extra wire on the stator and a regulator like the Wassel or Podtronics they do the same job as the Zennor.
All your 12v lamps will run on DC you will have to change the duck quack AC horn.
You don't have to buy DC lamps unless you want to use LEDs. The light switch ignition switch and believe it or not the loom will all work on DC.
Not having a go at anyone but this thread is very confusing, trying to explain it simply meant I had to keep filling holes so it may be one more confusing post.