Not quite correct.
The Lumen is the measurement of the total light output without directional information. It is a quantity of light (in roughly the same way that a gallon is a quantity of water).
The Candela is the measurement of the _intensity_ of light, usually in a particular _direction_. It is measured in terms of quantity of light per unit of solid angle. When you see a spotlight rated as 1 million candlepower, that means that in the bright part of the beam the intensity of light is 1 million lumens per steradian. (Note: the actual size of the beam is much less than 1 steradian, so that you don't have 1 million lumen. It is just like a car that gets 20 miles to the gallon when you only drive 1 mile.)
The Lux is the measurement of the light crossing a particular _area_, or light falling on a particular area. It is measured in terms of quantity of light per unit area.
They are all related by different measurements of space. A steradian is a measure of solid angle (think of a cone radiating from your light source.) The definition of a steradian is that on a sphere a cone with a solid angle of 1 radian with the tip right at the center of the sphere would cut out an area on the surface of the sphere equal to a square with a side that is the same as the radius of that sphere (whew!) Roughly if you have a cone with a solid angle of 1 steradian, it will cut 1 m^2 at a distance of 1 meter.
So if you have a light source that puts out 1 lumen/steradian (1 candela) then at a distance of 1 meter that light source will lay down 1 lumen/m^2, or 1 Lux at 1 Meter means an intensity of 1 Candela.
-Jon