With a projector that is just RGB and no White, such as a typical LCD projector, to get 2400 lumens, you pump 800 lumens of pure red, 800 lumens of green, and 800 lumens of blue. Bingo, 2400 lumens of white. (That's not technically correct, but let's go with it.) But what happens when you want to project a pure red on the screen, you know, an intense red, with no green or blue content? The more green and blue added in equal measure, the more pale the red, until you've added amounts equal to the red, and then your red is so pale - actually it's no longer red - it is white.
If we want pure red, as stated, you end up with 800 lumens of pure red. Not so for all projectors though.
With a typical single chip DLP projector though you might have 25% Red, 25% Green, 25% Blue, and 25 % White (clear) slices on the color filter. Well, the white segment is essentially red green and blue, so let's stick with our 2400 lumens example. For the 25% of the time that the wheel is on white, 600 lumens (2400x25%) make it through. Then 600 more for each of the others. Since we are only interested in pure red, and since the white slice is not pure, then one can't use the white filter at all. End result: for red, we get the time the red filter is "live" - 25%, so 25% * 2400 lumens = 600.
When the red filter's turn comes up, bingo, 600 lumens of red make it though. Wait - I just said only 600 lumens, not 800 lumens like an LCD or LCoS projector, The only way the DLP projector can find more red, is as part of the white segment, but with the red coming through the white segment, also come equal proportions of the green and blue. Basically we just can't put as bright a pure red on the screen. Adding white just dilutes it, so we can get 800 lumens of red, but only if we're also putting out 200 lumens each of green and blue, and in that case we no longer have the intense pure red desired.
Bottom line: 3LCD has said that having that clear slice on the color wheel prevents the white lumen reading, to accurately reflect a projector's color capabilities. I'd have to agree. That said, do we really need more lumens? Well, the adage says you can never have enough, which I generally agree with.
On the other hand, the average DLP projector for a given price and similar feature set, tends to cost a bit less, so it's not like there's a definitive advantage in overall brightness to either technology for a certain price. The thing is, if you never need more than those 600 lumens of red (or green, or blue), there's no difference. In that case a 2400 lumen DLP projector has enough pure red to do what is needed, even if the equivalent LCD projector can go brighter red.
One real point 3LCD makes does have some real significance: That when maximum brightness pure colors are called for, the DLP just won't be able to match the dynamics of the LCD projector. Just keep in mind that most colors we see in real life aren't pure colors, even the vivid greens of grass, has some blue and red content.
Another consideration is the effect of the clear slice - and its affect on color lumens, regarding the final image being projected.
This takes us beyond measurements into the physical impact of white being out of proportion to the individual pure colors.
Consider, one more time, our 2400 lumen sample projector with a 25% clear slice. If we go back to our assumption that we get 600 lumens of pure red and 2400 or white, that means that the white will be 1/3 brighter then it should be compared to that red. Theoretically, that would distort a photograph's colors relative to white. Those pure colors would not appear to be bright enough. Or, another way of putting it, the white might be glaring, by comparison. Slices of a pie chart placed on a white spreadsheet, be dimmer than intended compared to the white background or a white slice.