Is it a pipe-dream or can you really build a lathe made of hardwood? It sounds like a great project and I don't mean for it to be for constant, high-output use, just to turn the occasional spindle or bowl. Anyone have plans? (No, not a wooden motor!)
The Woodwright's Workbook: Further Explorations in Traditional Woodcraft by Roy Underhill (University of North Carolina Press 1986, ISBN 0-8078-1711-2) includes drawing and detailed construction narratives for 3 wooden lathes. One of these is a treadle lathe that could be easily adapted to use an electric motor. Your local library should have copies of all of Mr. Underhill's books.
"... and remember, there is no more important safety rule than to wear these - safety glasses."
Several things to remember when thinking about going this route (I did think about this for awhile myself)
1) Vibration is a killer for smooth turning, steel and iron weigh more and are denser than wood
2) For spindle turning, power is almost not important, but the important/limiting factor is distance between centers
3) for bowl and faceplate turning, the important factors would be motor power, swing (both over the ways and over the banjo(if inboard turning), and weight (Pivoting headstock or ability to move it down off the (opposite) end for outboard turning expands the effective swing.
Other things are also important, but those would be the first to come to mind. It all depends on your interest (e.g. bowls or spindles) and then it is a matter of the extent of the addiction.
The concept is fairly straightforward, but the execution is the key. I finally punted and bought a used Delta 46-700 lathe and built a heavy wooden stand and then filled it with about 650 pounds of sand and silicon carbide. It seems to work well, until I turn on a friends Oneway or Poolewood. I think in the end, it will be cheaper to buy one than to make one. Great starter lathes are the Jet or Delta mini/midi lathes and the jet 1236 lathe. I have turned on all three and like them a lot. Bowls need size (called swing) and weight to keep the lathe from doing a dance across the floor. (I know I can't dance with a person and I sure must have looked funny dancing with the lathe before I enclosed it and added the sand.)
Since all I do now is turn, I have a large shop full of great stuff that has a whole bunch of bowls on it. Oh well.