@Hodgman: I have this vague feeling that it's not my place to correct you, but since you asked...
A candela is roughly the brightness of a candle, measured in watts per steradian (solid angle).
You're mixing photometric and radiometric terminology, here.
Candela (cd) is the unit of luminous intensity (photometric).
The equivalent radiometric quantity is radiant intensity and it's unit is watts per steradian.
A lumen is candelas per solid angle.
Candela is lumen per solid angle.
You use this unit of measurement for lumimance (or the equivelent radiometric unit for radiance).
The unit of luminance (photometric) is: cd/m²
If I'm not totally mistaken, you can just plug the photometric units into the rendering equation.
For some reason the (English) rendering literature often uses the radiometric names for the quantities (radiance, irradiance, ...), but is using photometric units (lumen, candela, ...), which is totally confusing.
The radiometric units are used in radiation physics. The photometric units are used whenever the human perception is concerned.
(They just differ in the way how they weight light of different wavelengths. If you're not working with spectral lighting effects, you don't really need to care.)
The dot product formula you posted earlier is the photometric way of mixing RGB values into some luminance value (the weighting is according to the spectral response curves of the "average" eye).