Mystery Part... At least for me.

[Cullen]

Caroni,
The last picture (showing what I believe to be the top) looks very much like the tilting table for a grinder (to grind a relief angle on a tool bit). The horizontal slot is used to hold an adjustable guide that can be slid sideways to present the work to the wheel face for proper side relief. I have no idea as to where it might clamp onto a laythe, but Possibly it is a guide rest ( for your grinder) to sharpen laythe tool bits.
Cullen

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[benmychree]

It is a shaft vise for keyway milling; they come in pairs and are handy for milling long keyways and are nice because in especially horizontal mills, you can sneak up on the backside of it (the side opposite the clamp) with woodruff keyseat cutters, when normally a vise jaw is too wide for the cutter to reach the work. Yes, I have a pair of them ---

 

[george wilson]

From the bolt I thought the device was a lot smaller than it apparently is. Please post a common object at least,like a ball point pen if you don't have a ruler.