I don't really know what to call this and I can foresee this being a crazy idea, but hear me out.

A lion storage slot, which you have to purchase per account, maxed at 1 or 2. Essentially the lion is frozen when in there, will not be rolled over when you roll your account but can be removed a set amount of time later with all attributes the same as when you put them in. This is so that you don't have to send them to a frozen account or give up playing to freeze a lion until later.

Could be used to store a future king, a project lion, a special lion who you may want alive later, or a lion who needs apps from a later month. In order to prevent misuse I propose these restrictions:
-Slots have to be purchased for your lair and there are only 1 or 2 max
-Pay a small fee 1-3 Gb to put the lion in hibernation and maybe a small fee to take them out
-Once hibernating, a lion must stay in there a set amount of time (30 rollovers perhaps) They can stay longer but cannot be removed until the time is up
-(maybe) each lion can only hibernate once in their life
-No pregnant lions or lions with roles can hibernate
-Grandpaws and cubs not weaned cannot hibernate
-(potentially) Lethals cannot hibernate (But I would rather they could to give you time to get a jellyfish or canopic jar)

If you have any other ideas to add to modify and improve this, comment them below and I may add them to the suggestion