I'm able to download the lidar (.laz) and convert it successfully to a (.pod) in ORD. When I fit view, data is located in another State. My Coordinate system is "NAD83 State Plane Texas North Central FIPS 4202 Feet". Data is showing up in North Dakota.
Consider have at your disposal a feature manipulation engine like Safe FME. You will be able to read the lidar metadata in the file header and transform from one 2D projection to another. You might be able to safely transform in Global Mapper as well.