Being that auto-tune has enabled completely untalented singers to supersede talented and trained singers (and musicians) based on their physical attractiveness and stage persona, the inventor auto-tune should be sued for the damage he has caused to music competency and quality (and society in general). This suit would likely run in the billions.
Provided that Apple are not infringing on any patents that auto-tune registered against their product, there should be no reason for them to be sued. Apple have proven that they can develop high quality products, therefore they may be able to offer an even better alternative product to auto-tune. If auto-tune feel threatened by Apple's product, that should inspire them to continue to develop their own product to ensure they maintain their share of the market for such products.
Auto-tune isn't a thing that was "invented" but rather a technique that is invented. A technique can not be owned. Is there an owner for the way you should hold a golf-club to accomplish a fade? Of course not. Techniques should not be owned just because they are instantiated in code.
As long as Apple's newly acquired competing product does not infringe upon auto-tune patent and copyright, there is no reason for the people of auto-tune to sue. The American free market welcomes competition, and this purchase (and subsequent growth) by Apple could aid in products becoming more efficient and/or affordable!
The only demeanor for suing Apple, in my opinion, would be if there was a breach of contract. I did not locate any information on the collaboration with Apple ever being attained or detained. Apple may only be sued if they did not CYA (cover your a**) or nor did Hilderbrand.