My suggestion will be to contact you service rep or IBM to obtain the information. IBM should have this information for you.
Without obtaining the license keys from IBM which can be done via the web or by calling IBM support to get the keys, you need to reload the system from your last full system save which will have the license keys attached. There is no way of pulling just the license keys off the full system save tape.
As long as the versions are the same then perfroming a full system restore of the OS will be the only way of getting the keys included.
You could perform a save of the user libraries SAVLIB and SAV of the folders and IFS entries and then scratch the system perform a restore of the OS and then restore the rest of the system that you saved above.
Without the paper keys or access to the license key website, this is the only way that I know of.
Let me also clarify that the LIC does not have a license key, it is the actual OS 5722SS1 and some of the other OS program products like Media and Storage Extentions that have keys. If you WRKLICINF you will see all the products that need keys.