Cleaning out my garage and finding lots of things stashed away. This was my grandfather's and I assume it came off a lathe? Would it be specific to a certain lathe? Is it still useful or have much value? Planning to offer it to anyone here first before throwing it at ebay.

Yes.  Wood lathe.  Used for bowl turning and the like.  It screws on to the lathe spindle, and the various jaws fit into a shallow opening you turn in the wood being worked, then open to clamp inside the opening when you turn the collar.  Still very useful.  If I were turning, I'd have been on it before I even finished reading the message.  The Sorby chuck was one of the respected chucks in its day.

Because it screws on to the spindle, you should look at the papers that came with it to see if you can figure out the thread size and pitch (number of threads per inch) it will fit.  Some of those chucks were designed to take an insert for the threaded part, so you could get the chuck and the insert(s) for your lathe(s).  If that's the case, and if this one has an insert, the insert itself will probably show the thread specs.  Adding that information here will help those who are interested; if you wind up putting it on the Bay, that will be a critical piece of information.

Dang.  You're making me wish I was still turning.

Wow, thank you! That actually really makes me wish I had a lathe- I've wanted to make a bowl for a long time... Have some big chunks of burl I've cut off trees.

I read through the manual- just discusses the different attachments. No mention of threads anywhere.

Look at the part with the shiny collar threaded on one end - check out the hole at the other end from the collar.  Is it threaded, and are those threads clearly part of the surrounding metal?  If so, you've got a fixed thread size.  Or, is there evidence that those threads are a separate part?  If so, insert.

Sears used 3/4" - 16 threads on their lathes for years.  This is a standard (fine thread) thread size/pitch, so if you can find a hardware store (or a bolt-and-steel store) with large bolts in both coarse and fine thread, take your chuck in and see if one will fit.  The second most common size/pitch on American lathes is 1" - 8 (a standard coarse thread).  If the 3/4" bolt slops around in the hole, try a 1" - 8 bolt.

The Sears lathes are kind of lightweight, so don't let your ownership of this chuck drive you in a decision to buy a lathe.  You might be better off selling this one and using it to help fund a mid-weight lathe, like an older Delta.  Those chucks are cool, but turners got along for generations without them.