On the front I use a headlight from brightbikelights.com attaching the light directly to the handlebars via the rubber ring and the battery pack via velcro to the handlebars. Position it away from the stem for clearance from the front wheel when folded. This approach should work with any compact front light.
The rear light is more challenging. I have a 2017 saddle with a screw underneath for mounting a bracket so I have purchased this:
https://brilliantbikes.co.uk/brompt...rompton-cateye-saddle-mounted-rear-light.html
If you have other cateye lights (who doesn't?!), all you need is the mount, if you can find it.
Having a "Cadbury's Quality Street" tin full of functioning bike lights attaching to the rear seat post, I also bought this:
http://www.ebay.co.uk/itm/192078358128
I removed the reflector on the rear rack and added this instead onto which my Smart light fitted without affecting the fold. Result! I replaced the reflector, attaching by a single screw and now oriented diagonally.
Another option is clothes-mounted rear lights & helmet lights.
There's also brackets and lights which attach underneath the saddle onto the rails for pre-2017 saddles or non-Brompton saddles. Brompton also make a rear light which replaces the reflector for £15.