To lean in a controlled way it is best to have a vernier mixture adjustment and a multicylinder engine monitor such as the JPI or EI instruments. It is very doubtful that a carburettor Lycoming can be efficiently leaned as the mixture distribution to each cylinder is appalling. The risk is that it is possible to push the leanest cylinder into overheating. Robinsons only have one head temp probe which may not be on the hottest/leanest cylinder. It is possible to cause damage by overheating without detonation. 400 deg F should be considered a practical maximum cruising head temp and it is easy to exceed this by leaning.
Injected engines are a bit better but unless the injector nozzles are matched to provide the correct flow for each cylinder, overheating one or more cylinders is still possible unless all the head temps are monitored.
Leaning is permitted with Enstroms and I always lean aggressively. It is possible to drop the fuel consumption from 14 gph to 10 and run with lower cylinder head temps. I generally run the hottest head at 350-360 deg F. I use the techniques described by John Deakin. (see below)
With a properly set up injection system it is possible to lean safely and efficiently. It is almost impossible to stop an engine by overleaning as the power drop off alerts the pilot in good time.
Leaning is also demanding of pilot attention to do it correctly.
The risk is the brainstorm when returning to full rich, when one pulls the knob instead of pushing it. I know - I have done it. The engine stops.
Robinsons are not equipped for leaning and to do so without the appropriate instrument/control is fraught with pitfalls. The Raven2 could be modified for safe and successful in flight leaning but unless it was, I wouldn't do it.
I would think a properly modified, leaned Raven 2 would cruise on 12 U.S. gallons per hour. Was Jennifer Murrays aircraft modified?
John Deakin has written lots on this subject and before anyone considers leaning a Robbie, a bit of time reading these articles is recommended.
http://www.avweb.com/news/columns/182544-1.html