3.7 Budget Tornado Shot!

Lioneyes fall is one of the items you can actually farm in this game. There is a Divination Card The Lion that can be exchanged for a random unique item with "lioneye" in it's name. There are currently 5 uniques with Lioneye in their name, so your chance to get the jewel is not too low.

The Divination Card drops on Glacier and Caldera maps but I've done tons of glacier maps without finding a single The Lion and Caldera is kinda high to farm on it if you don't have very good gear.

That said, there is actually a third source for the Card. I am talking about The dishonoured Queen, a unique mob found in The Mud Flats in act 6.

If you enter the mud flats from The Karui Fortress, head right and follow the upper wall. You will find her easily. Run back to the Karui Fortress, open a new mud flats instance by clicking the entrance while holding ctrl. Kill her. Repeat.

I am currently farming her on my level 75 ssf Deadeye. I farmed 3 Sets of Cards so far. No luck till now, but you get the cards fast (I'd say 2-3 Sets in an hour of straight farming) if you do it with a character in the right level range or a very fast character with increased quantity.
That said, you shouldnt expect to get it too fast. Others farmed it in ssf and they got the jewel after handing in 12 sets. That's still a lot of time and I guess you can make much more currency than you need to buy the jewel in that time if you farm other areas.

Anyways. You can get it, even if you don't feel like spending 90 chaos.

Edit: Took me 6 Sets of Cards to get it. Was a little less than 3 hours farming for me. Cheers.