If you lean, the rpm increases as flame front propagation speeds up (mixture burns faster), until the mixture leans to stoichiometry - the ideal mixture. If you keep going past that and lean more, the rpm drops again as flame propagation slows again - to the point where it is required to open the throttle to maintain RPM.
As Nick said it is quite possible to run a piston lean. A few years ago I decided to utilise the techniques favoured by John Deakin and run lean of peak EGT. This yields a fuel saving of around 30 to 35% from full rich. My Lycoming runs smooth to about 70 deg on the lean side but it took a huge amount of work to get it to run right. I usually run 50 degrees lean of peak. The data from the engine monitor is stored and periodically checked against reference flights to make sure all stays in tune. It aint exactly a technique for low hour or Robbie pilots.
I did my LPC last week and it even makes the examiner squirm uncomfortably when I pull the mixture out 2 inches and open the throttle wide at 1000 feet.
Ive been doing it for 4 years and it's saved me a fortune. It was worth the effort. The engine runs cool, clean and produces no carbon monoxide. cabin levels drop from 30-50 ppm when rich to zero when lean. It would save a hell of a lot of avgas if it could be done automatically on all pistons. We are indeed still in the dark ages.
To read John Deakins brilliant work (if you have a few hours spare) goto
http://www.avweb.com/news/pelican/list.html the early articles go through the basics. Number 18 is a good place to start. You have to register to read the articles.