Not as low as 10 meters, no, because the surface of the Moon varies by much more than that. But you can get pretty low orbits.
Here for example is an orbit with initial average altitude of 124 km (semimajor axis 1861 km) and stable for 4000 days, or about ten years.
"We found frozen orbits with initial eccentricity equal to 0.02 that can be applied for missions of long period without the needs for doing orbit corrections for a period of very long time (larger than 4000 days). The initial orbit with appropriate characteristics can extend the time life and reduce maintenance costs."
It's a major challenge because of the Mascons - shown here in red - these make it difficult for a satellite to stay in orbit around the Moon long term, unless it is in a very special orbit.
"There are actually a number of 'frozen orbits' where a spacecraft can stay in a low lunar orbit indefinitely. They occur at four inclinations: 27º, 50º, 76º, and 86º"—the last one being nearly over the lunar poles."
-http://science.nasa.gov/science-...
You get lower orbits also. I'm not sure what is the lowest known stable orbit you can put a satellite into around the Moon, stable for more than a month or so.
There is an orbit in this paper, involving two satellites joined together with a 50 km tether in orbit around the Moon which take them to within 10 kilometers of the surface. http://oa.upm.es/33097/1/INVE_ME...
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