Hello,
finally! The latest release of LAStools (160721) marks the first attempt to also output projection information via PRJ files for all vector derivates (in SHP format) and all raster derivatives (in BIL, ASC, FLT, and XYZ formats). As always you can download LAStools via the link provided here:
Tests on my end show that the generated PRJ files for common projections are correctly read by QGIS. Could you test whether your projections also get parsed correctly when loading SHP or BIL files into QGIS and ArghhGIS? If they don't please report back to me with a (tiny) example.
Regards,
Martin @rapidlasso