I started using DeGussa synthetic ruby stones many years ago. Very expensive but also very good.
They can be viewed by googling Paul Gesswein.
The finer grits can be cleaned up with an ordinary white rubber eraser. Another good choice is Spic and Span or Comet mixed into a medium slurry and rubbed on the stone with your thumb or finger.
The coarser stones will gradually lose the sharpness needed to cut.
You can restore them by using a glass plate and something like 140 mesh boron carbide powder.
The drill is to place the pane of glass into a cardboard box and cover with a light layer of boron carbide.
Place the stone on the glass and begin describing a figure eight motion and press down fairly firmly.
You will feel the boron carbide break down as the ruby is rubbed against it.
The powder will break down quickly and must be replaced.
Luckily, you do not have to do that too often.
Depending on where you work, you might have access to a grit blast machine.
That media will also work. If you are careful, you can even grit blast the stones themselves but you will end up abrading the edges and destroying the flatness and make the stone convex.
If you are using them as hand lappers, it does not really matter.
If you are using either hard or soft Arkansas stones, you can clean them just fine with a little Comet or Spic and Span into a slurry.
Arkansas stones are really pretty soft and do not cut well. They do provide a good polish.
The DMT double edge diamond files are my choice for sharpening edges on knives.
I have had mine for years and got them from Smoky Mountain Knife Works.
The DeGussa pure sintered aluminum oxide are the best I have ever used but you will pay and pay dearly for them.
A standard 4X1X.5 pocket stone will probably run you $150 or more.
Here is a link.