HDR Light Studio project data does not transfer over to duplicated levels
If you have lighting made with HDR Light Studio in your level and you duplicate or use 'Save Current Level As...' to save your level under a different name, then the HDR Light Studio project data will not transfer over from the original level.
Temporary workaround:
Open your original level in Unreal Engine 5 that contains your HDR Light Studio lighting. Start HDR Light Studio in connection with Unreal Engine 5 and save your lighting project from the HDR Light Studio interface as an .HDi file (Project > Save Project As). Return to Unreal Engine 5 and stop HDR Light Studio from the connection panel. Next, open your new (duplicated) level in Unreal Engine 5 and start HDR Light Studio from the connection panel. Then, load the project (.HDi file) from the HDR Light Studio interface using Project > Open Project. The lighting design will load into HDR Light Studio replacing its current design, and will then be synced back into your duplicated level in Unreal Engine 5.