Normally I assign the coordinate system at the lasd level, after loading the las files into it.
I have rarely met a las file that has had coordinate information already attached to it.
So, you should really go back to that Gov agency and find out what the correct coordinate system for their data actually is.
But as Adrian says, if it is pitching up off the Nigerian coast, then maybe it is in GCS (geographic) and not a projected system. That is quite unusual.