The above works, here are a few more directions for clarity:
At the USGS Lidar Explorer Map, click into the "product metadata" (third option under Original Metadata), not the Lidar Metadata which is a dead link at present, and search for the string PROJCS to find the coordinate system. You can copy and paste the name of the specific NAD 1983 projection at the ArcGIS website I'm linking below and then use the four digit code the chart shows you within the Map > Properties >Coordinate Systems search bar. So for the example above, if you search the document and find the ID of 2872, that will bring you right to NAD 1983 HARN StatePlane California III FIPS 0403 Feet.
https://help.arcgis.com/en/arcgisexplorer/900/ArcGISExplorer/sdk/html/3d2c0d49-513c-a897-95bc-d4774c...