I was a Machinist for 46 years,,,,,,,,,,,,,, I know what I'm doingDepends on the grit used.
Machinist generally use the figure eight on larger items. If you don't know what you are doing, it is easy to rock something as small as a tip, which will create the convex shape the op is describing.
Lapping on a diamond plate is pretty foolproof. The number of strokes isn't really a concern, I have enough stamina and time to spend seven seconds on prepping a tip.