I recently decided to upgrade my lighting, and I went with a Lezyne Super Drive. It looked like a good option, and I like that it uses an 18650 battery so that I can carry spares. It turns out that neither of the mounts work for my handlebars though; my bar is too thin and the mount won't close on it securely.

Does anyone have a recommendation for a light that comes with a mount that would work on thinner handlebars? I don't know the exact size of the bar, but it looks like the small lezyne mount is 25.4 mm, so the bars are smaller than that.

Keep the Lezyne. Take the DIY route that people use to mount tail lights to rack leg struts. You'll need some electrical tape and an old inner tube.

A small section of tape goes on one end of the tube (the other to the bar/tape), to keep it from spinning. Wrap the tube around until you're just a bit larger than what you need. Then pull the tube to compress it down. Add another bit of tape to hold the tube to itself. Or depending on how much you have to shim up, you could just get by with some electrical friction tape.

+1

https://www.ayup-lights.com/

Go the a hardware or auto store and find a piece of tubing of the right wall thickness to shim under the light mount. Slit a short segment longitudinally and put it on the bars under the mount.

Many of the lights I have purchased come with a strip of rubbery material that you can use as a shim.