In ArcGIS Pro 2.5 GP-tool "Convert LAS" returns "ERROR 000522: Unknown coordinate system for input dataset" if a LAZ does not have a defined projection.
"3D Sample Tools/ Conversion/LAZ to zLAS" does not need the LAZ file to have a prj, also you can specify the missing projection when running the tool.
Enhancement Request: Allow ArcGIS Pro/Conversion/Convert LAS to work with LAZ files without a prj and let the user define which prj to apply to the output LAS or zLAS file.