Doubtful
I know that Lynx is the most obvious moniker, as it's the one of the few big cats left; however, it seems very unlikely that Apple would chose this, owing to it's visual similarity to Linux. Two operating systems with similar names makes absolutely no sense from a marketing standpoint, particularly when Apple could name it pretty much anything else and avoid the problem entirely. (I suspect this is the reason that Apple has eschewed it as a convention thus far.)
Regardless of what it's called, I hope that Apple gets its act together. Neither iOS nor OS X still hold the edge they once had against their competitors. I just bought a Windows 8 Phone and, while it's certainly not perfect, I must say that much of experience is better than anything I've had on an iDevice. Like OS X recently, iOS has added relatively meager UI enhancements since it's release. Apple spent so much time obsessing over the margins that it it took forever to get basic functions like copy and paste. And, in my estimation, the last truly outstanding update to OS X was Tiger. Since then, Apple's done little more than slim down the file system, add some pointless eye candy, and convolute the platform by adding features designed for a mobile environment. (Eg. Launchpad, which at worst is utterly useless and, at best, no better than simply putting a folder in your dock.)
OS X used to be, far and away, the best desktop experience, period. It's really sad that Apple's fallen so in love with it's own image, that they've substituted branding for innovation.