A habit of being an asshole is not cost effective to fix. And giving validation to their belief that they should have "important jobs" just gives them real power to bully you more.
Instead of rewarding bad behaviour, they need an unambiguous dressing down from someone they respect, and a PIP. But IME it's a waste of time, rip the bandaid off and get someone with better default settings.
I think this guy's manager said he won't fire or move him. So then if to avoid sabotage you must respect him and give him important tasks then that's what you do. Even if you think it harms the company. Then you show how it harm the company and you win.
But at least try the non-confrontational 'lets have a coffee' approach first, especially if OP is their superior (which by the other comments, OP is).
Also, it feels like that guy is defensive and feeling butthurt. So op can try pretend he's awesome and give him all the difficult tasks to prove. If he fails you know what to do. If he is good then less work for you.
As the lead you don't need to be always the rockstar, the coolest managers are the ones create chance for teammates to be rockstars.
(I had bad leads where it just felt like what is the point for me existing here as a code monkey if this guy sorted it all. Tho I would never sabotage it. I just quit;))