Preface: I know there are a ton of suggestions already posted for how to “fix” the economy. I don’t pretend to be any smarter than anyone else who has put forward an idea on that score. In fact, I’m pretty sure there just isn’t a “perfect” solution. But I have spent some time reading the feedback the other ideas have gotten and thinking about what’s being said. It seems to me that any system to remove lions from the economy must:
1)Have an incentive for people to use it. “Chasing” lions for no reward isn’t working- people just aren’t using it enough.
2)Not add SB to the economy.
3)Discourage/disallow people from taking unfair advantage (“gaming” the system) by claiming a bunch of NCL’s and turning them in for rewards instead of buying bred cubs.
Hopefully, my idea will accomplish... at least some of those things. ^_^;

The Mysterious Stranger
If the lands become overcrowded with lions, the balance will be destroyed and all will suffer. In the name of preventing this catastrophe, a mysterious gray lioness is willing to guide surplus lions from your pride to a new home far away. You will never see them again, but in exchange for assigning your pride members to her custody, she offers various trinkets (decors, titles, and such) for sale in her shop. While I came up with this beforehand, this would be very similar to how the Shaman shop works in this month’s event.

Unlike the Celestial Stone, which killed a lion and gave you a random reward of XP or SB, this lioness just shuffles the lions off to parts unknown (this allows players to imagine whatever fate they want for their lions). The Stranger offers tokens in exchange for these lions. But how much is a lion worth?

Each lion would be worth a base amount of tokens (The exact amount would be up to the admins to determine, but for our example, let’s say 5 tokens for any lion.). It doesn’t matter if this lion is an NCL you just pulled off the savannah or a beautiful pedigreed cub, you get at least 10 tokens for it every time. If the lion has more than 3 markings, however, you get a small bonus (to keep my math easy, 5 tokens.) You would also get a bonus if the lion had more than 100 stats (This bonus should be the same as the marking bonus, so in our example, 5.) If the lion has 3 markings AND 100+ stats you get both bonuses, for a total of 15 tokens where an NCL (for example) would be worth only 5. The exact numbers are, again, up for debate but they should pan out in roughly that way- gathering NCLs to turn in should be an option, but not a very good one.

The standard bonus system could concievably be more granular, but it is hard to balance rewarding appearance-breeders with stat-breeders in that regard, since each lion can only have a max of 10 markings and each lion can have theoretically infinite stats (among other reasons). That is why in this initial pitch I've only included one tier of marking-bonus and one tier of stat bonus. However, the following additional system would serve to augment the rewards for appearance-breeders and stat-breeders in a fair way:

Sometimes the Mysterious Stranger has something special in mind. She won’t reveal her reasons, but occasionally she might especially desire any number of traits: acertain mark, a specific fertility, males, females, a certain range of stats (ex: 350-600- could be anything, though), a certain threshold of stats (anything over 300), a certain base, mane, or eye color, or a combination of the above. If your lion happens to meet her special criteria, you get an additional bonus. (I’m still undecided on whether this bonus should be the same every time, or if it should change depending on how much of a rarity her request would be, allowing players to very very rarely hit the jackpot). The Stranger should only change her criteria on Fridays, and they should be announced in the News post so everyone is aware of what she wants.

This system does not unfairly penalize new players or folks with atypical tastes. It rewards those who breed for appearance or stats (or both). While NCLs have some slight value, enabling newbies to maybe make some money selling NCLs, they are not so valuable as to unbalance the system completely. There is also an element of luck, in that if you happen to have a lion the Stranger especially wants you can get even more tokens than you otherwise would.

Here are some things the store might sell (Thank you to Roka, Dunnart, and Blooming~Iris for suggestions):

MAYBE: base changers, mane changers, and other items available in either the Oasis or Monkey Business. I’m not sure that’s a good idea, because selling GB items would take revenue away from the site and selling SB items would devalue the SB sink that is Monkey Business, worsening the glut of SB in the system. While it might not be a good idea to incorporate such items, it is a possibility so I have listed it here.

XP granting items, on the order of coconuts or broken drones.
Food with a higher chance to grant stats than usual prey.

More cheaply than the special food, food bundles or normal carcasses as well. (Tyrrlin)
A monthly special could be out of season event marking applicators (these would have to be pricey) (Blooming~Iris).
Tokens could be for sale for SB at a high price. This would not overly devalue tokens if the token prices for other items were high enough (Roka).
A modification to this idea: Perhaps there could be a bundle available for sale for SB that includes a random amount of tokens, introducing a fun element of uncertainty into how many you might get (MysticSky). Maybe the bundle could also contain some food or toys as well.

Decors:
Footprints of the Departed-A clay rock in which lions have left pawprints as keepsakes before leaving
They Grow Up So Fast- Baby teeth from cubs that have grown and left (scattered on the ground or maybe as some kind of jewelry?)
Braided Keepsake- Locks of hair (again for the ground or possibly as jewelry)
Trophies of the Culled-Lion cub skulls (Dunnart)
Trepidation- Sad facial expression (Dunnart)
Relief- Relieved/relaxed facial expression (Dunnart)
The Spared- Relieved/chilling lioness (Dunnart)
Ill-Gotten Gains- Broken/gnawed on toys (Dunnart)
Unloved decor (lioness skull?) (Blooming~Iris)
Violent Slap decor (bruised and bloody claw mark down cheek?) (Blooming~Iris)
Abandoned ________ (a lion or lioness walking away in the background?) (Blooming~Iris)
Farewell to You Background (lioness's walking away in the background, rainy maybe?) (Blooming~Iris)
Greener Pastures (a background with lots of beautiful green grass and flowers with mountains in the distance)
Bright Future (a background with a sunrise theme)
Fond Farewells (a sunny background with a grassy field with a path leading off towards distant mountains)

Achievements:
Farewell Forever My Love: achievement for giving up X amount of lionesses (Blooming~Iris)
Get Away From Me You Heathen!: achievement for chasing X amount of males (Blooming~Iris)
Your Mother Doesn't Love you/Future Abandonment Issues: achievement for chasing X amount of cubs. (Blooming~Iris)

Titles:
Chaser, ______ (Blooming~Iris)
King of Running Off (Blooming~Iris)
Stranger Danger (Blooming~Iris)
"the Pragmatic"
King of Fond Farewells
LupineEyes[Raiven] suggest having some that are specifically for good or bad karma (as in, there would also be a karma threshold one would have to meet to use them):
Bad
Demonic _____
Killer/Murderer, _____
_____, the Sacrificer

Good
Angelic _____
Savior _____
_____, the Guide

There are some things about this idea that I'm unsure on. For one, it's a lot of coding. But any new feature would be. It's also another currency, but given that each new event seems to have its own currency it seems the Devs are not shy about that. But also, it might take some trial and error to hit upon the correct "value" for a given lion to keep the economy in balance.

TL;DR: Sell your lion to an NPC in exchange for tokens (not SB, not GB, something else). Any lion that’s breathing is worth a base amount. Lions with stats above a certain threshold earn a bonus, lions with more than 3 marks earn a bonus. Additionally, the NPC sometimes has special requests- if your lion meets the NPC’s criteria, the lion is worth even more while the “special” is active. Once you have accumulated enough, use those tokens to buy shiny things like decors or titles.

Thanks to those who have made suggestions!
Whispermouse
Knoka
Larvirawr
Roka
Blooming~Iris
LupineEyes
Tyrrlin
Dunnart
MysticSky