The correct term is motion blur. The object/frame is blurred due to motion while the shutter is open. The concept doesn't change just because the shutter is open 1s instead of 1ms
As dougal says, luxrender doesn't handle complicated motions during exposure. As such I think luxmerger could be a viable alternative. In this case, it is crucial that each frame is rendered with the same number of samples/pixel as all the others (otherwise noise will be unevenly distributed). Steps:
Set up a haltspp count (could be fairly low if you render a large number of frames)
Export the animation and render. Contrary to normal animations, you should NOT
use the "fixed seed" parameter during rendering.
Finally use luxmerger to merge all the frames. If you're running low on disk space, you could merge the flm's after each frame, ie "luxmerger -o master.flm frame0102.flm master.flm".
Rendering and merging may be best handled by a small script.
If you're using a high number of frames (for something like your initial picture, I'd try around 500-1000 frames), you should be able to set haltspp to a very low number. I'd try 10 first. If you're not satisfied, just render the animation again and merge the resulting flm's from the two runs. If you wish to render the second run at a higher haltspp, you can do so, however just make sure ALL the frames in the second run are rendered with the new haltspp.
May contain traces of nuts.