In industrial applications probably the closest approximation is in dressing bonded abrasive wheels. These use abrasive particles including aluminum oxide but a different bonding medium which makes them a bit tougher than standard fire bricks. With this is mind a diamond tipped dressing tool would probably be a good thing to try.
I lathe turning stone scrapers are widely used. In this case a tough, abrasion resistant tool steel would probably be the best bet perhaps something like D2.
Similarly for turning it is probably well worth sawing the outside to a hex shape to get the section closer to round before you start.
Another approach would be to use a belt linisher with a coarse ceramic belt and a cylindrical grinding jig.
Of course if you just want a simple cylinder it would be logical to use core drills for both the inside and outside. In this case you might want to pre drill a pilot hole in the centre and fit a metal sleeve and use a plain pin instead of the pilot drill in the arbour.
Another big consideration is dust extraction to protect both the machine tool and your lungs a firebrick dust will wreak havoc on both.