Parallels Desktop Lite is App Store product.
In order to use it, you have to do in-app purchase (a subscription). In-app purchases are not a subject to Family sharing at the moment: https://support.apple.com/en-us/HT203046
You can restore in-app purchases on the devices associated with your Apple ID.
In order to avoid the impossibility of the device association with another Apple ID, please do not use the purchase restoring option for devices which aren't associated with your Apple ID: https://support.apple.com/en-us/HT204074