This question keeps coming up: the focal plane shutter and moving mirror of an SLR both block the sensor except when the photo is being taken. To get live LCD preview one needs to solve both problems
a) the mirror problem: either retract it in advance for LCD use, or use a fixed partially reflecting mirror as in the Olympus E10/E20
the focal plane shutter problem: fixed lens digital cameras including the E10/E20 use a between the lens ("leaf") shutter instead, which has the downside of restricting maximum shutter speed and being expensive and not backward compatible with existing 35mm format SLR lenses; opening the FP shutter in advance and using "electronic shutter" operation by the sensor alone is a future possibility.
I hope for a niche market of high quality true rangefinder-like cameras with compact LCD viewfinders, building on designs like the Olympus E20 or Canon G3, for the virtues of that pivoting "digital successor of the ground glass viewfinder", plus fast, quiet operation (no mirror noise or lag) in a relatively small "candid camera" format.
Leica themselves are trying such a camera, with a big 2.5 inch LCD, but they have said that their existing M lenses are incompatable with digital (light strikes the sensor at a far more severe angle than in SLR's). Thus the Olympus E10/20 approach of an extensive supplementary lens line might be the best bet in the near future for getting a lens variety matching or exceeding what rangefinder cameras offer, and also for keeping dust of the sensor.