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Update: So in all of my obvious searching, I forgot to check the Logan FAQ. They state very plainly that "All other oil spots (besides the ways) on the Logan Lathe can be oiled with ISO 22 grade spindle oil"...so according to the .pdf that Dave posted, it would be the Mobil Velocite No.10 oil.
is that keyway shape next to the shaft a recess like that can have a felt pad to hold oil John