Is there any public or private sources of LIDAR data in Japan? Searching online did not lead me to any sources.
I am not sure what website have you looked for it but here is the list:
http://opentopo.sdsc.edu/datasets?listAll=true ---> it's not there yet but keep an eye
if it is not what you look or find for a specific of area for Japan, I would recommend that you to contact someone in Japan that might know of for free. You can contact USGS or NASA for more information.
Good luck !