This is a vintage clock/watch makers lathe, with other accesories.
Made by LME, London N8. Lathe No 1050.
Everything looks to be in really nice order, but please study all the pics carefully - this is not a field that I am familiar with and I really am not sure what most of this stuff is.
It looks to me that the box with one missing piece in - that piece might be in the lathe.