Use the lion token on the puzzle to see what happens. Ah, I see. As you saw in the note on Soren's tablet, the goal is to turn all the lion heads so they're face up. Read to the end of this hint for a step by step.
I hate this kind of puzzle, I really do. It drives me crazy to get a puzzle half solved and then find out that every other move undoes all my hard work. But maybe that's just me.
The rule here seems to be that if a lion head is face up, it sends the token to the left; if it's face down, the piece goes to the right.
But every time the token goes by, it flips the lion head so the next token will be sent the other way.
A little planning ahead will save you the kind of cussing I do. Before you drop in the token, imagine how it's going to travel and what it's going to do to the lion heads after it's gone through.
Any way you do this works, but here's the fastest way through I've found:
Drop the token in these slots: 1, 2, 2, 3, 2, 2, 2. This works for the original arrangement where all the heads are upside down; if you've been messing about, press the Reset button before you start.
When you're done, the puzzle pops open to reveal a wooden gear. Snag it.