Two Questions - Drilling Hss & Lathe Lubrication.

[CHJ]

This is a 2nd blade which broke when I dropped it on the floor. You can just see the small hole, drilled with a spearpoint TCT glass bit, in the corner of the smaller piece,

Would be a bit nervous about the suitability of that material for your parting tool if it is that brittle that it snapped when dropped on the floor. It's a sure fact sooner or later you are going to subject it to a far greater stress using it on the lathe, albeit unintentionally.