When I bought my lathe in an estate sale, it came with all kinds of hand ground tool bits and gadgets. Most of the stuff I could identify, but there are a couple of items that I am not sure what they are used for. The pointy thing is approximatly 1.5" long and 0.1875 DIA (slight taper) with internal threads.
The other object is about 3" long with largest DIA of about 0.250
Pictures are at: