I’ve been looking for the Barlow lens just not sure of the right one.I have a B&L StereoZoom 4 and, as Sam said, the problem to add a ring light to it is its shape.
You must add an accessory to it to be able to attach the light. I was lucky enough to find a glass (just a simple glass, no a lens) to protect the optics from the fumes produced when soldering electronics under the microscope. There are also Barlow lenses for these microscopes.
Another problem that you will face id that the ring light will take some of your working distance because the microscope's objective will not pass through the internal diameter of the ring light.
In the case of my light it would take as much as 40 mm of your working distance what will make it unusable unless you have a Barlow lens of 0.5X or even better 0.3X.
Perhaps it will be better for you to look for a dual gooseneck illuminator.