The play's allegory

the definition of allegory : a story, poem, or picture which can be interpreted to reveal a hidden meaning, typically a moral or political one.

The Lion and The Ass
Well anyway, one year, as every year, all the beasts of the valley were invited up to the sanctuary on the top of the mountain for the blessing of the animals. The lion chose the donkey as his travelling companion, because he thought: "This journey is going to be long and wearisome, and when the going starts to get steep I can get up on the donkey's back. He can carry me. And then, if I happen to get hungry, I can eat him too!" So he suggests to the donkey that they travel together, and the donkey agrees. But the donkey proposes a deal: "We'll take turns in carrying each other. Alright? Two miles each." So off they go. When the road starts to get steeper, up speaks the lion: "Time for me to get up on your back!" "Alright, up you go...?" And with a leap the lion is up there on the donkey's back. "Hey, go easy with those claws sticking into my ribs," says the donkey. "You scratch me like that and I bleed to death!" "I can't help it. I have to hold on as best I can! Giddy-up! Giddy-up! Away you go!" So the donkey reaches the top of the mountain, and by this time he's got blood pouring down from his scratches. "Well," he says, "now at least for the journey down it's my turn to ride on your back!" "True enough, fair's fair," says the lion. "You did the work on the way up, I do it on the way down. Away you go!" And the donkey jumps up onto the lion's back... But he has a terrible time keeping his balance. He slithers here and there, because he's got hooves, you see, and he can't get a proper grip. Then all of a sudden our donkey jockey has an idea – a thrust of his loins, stiff as a ramrod, and straight up the lion’s backside. Held in place. Good and solid. "Hey, ho, ouch!" shouts the lion. "What is that blooming great truncheon that you've stuck up my rear?" Forgive me, your majesty...” says the donkey. “I can’t help it – each of us has to hold on as best he can! Giddy-up! Giddy-up! Away you go!"

The obvious link this story has to the play is that the ass gets a grip of the lion because he goes up its backside and one of the devils possesses the wrong person that way. 
The lion seems to be the clever animal at first because it thinks of this plan to have its own way but the unexpected happens when he doesn't succeed in what he thought he'd do and instead, the lion gets punished with his 'own medicine'. All in all i think the message to it is to don't be over-optimistic in what you think will happen because it could lead to a wrong turn. Or don't do something in the first place if it's wrong and you're feeling certain it'll go to plan.