At those conditions, "lubricant" is probably the wrong way to think about it.
Those pressures, rates of fluid flow, and shaft rpms is going to result in the mechanical surfaces being separated by hydrodynamic forces and/or boundary layer flow.
Technically, lubrication is the same physical principles, but viscosity, weight, chemical stability/ durability and other factors become more important for lubricants that are recirculating.
(Oil in eg, a 4-stroke engine operates on these principles, with the rotating shaft causing pressure differences in the oil that "lift" the shaft from contact with the surrounding metal, until pressure (and therefore spacing) is roughly equal on all sides.
A ping-pong ball floating on a column of air self-stabilizes in the same way.)
The primary concern for these turbopumps becomes heat. So heat transfer and temperature of the "lubricating" fluid become more important than its other nominative qualities as a lubricant. Fluids being pumped at cryogenic temperatures can obviously help here.
So instead of a normal "lubricant", most of these turbopump designs just run a portion of the fuel/oxidizer fluid through the critical areas to provide the surface separation and cooling required.
The documents in the nasa links below don't seem to agree witht this. Actually they are not fluid bearings, they're ball bearings and mechanical surface wear was a big problem for the oxidizer pump bearings in particular because of the lack of good oxidizer compatible lubricants.
Ball bearings require "lubrication", and the lack of good lubricants is exactly why they use fluids that end up behaving as I described, and why "lubricant" is the wrong way to think of it in this case.
If anything, the existence of a good lubricant would prevent the surface wear. Temp control and fluid dynamics are what they have to work with, and yes it results in surface wear because it's suboptimal.
Those pressures, rates of fluid flow, and shaft rpms is going to result in the mechanical surfaces being separated by hydrodynamic forces and/or boundary layer flow.
Technically, lubrication is the same physical principles, but viscosity, weight, chemical stability/ durability and other factors become more important for lubricants that are recirculating.
(Oil in eg, a 4-stroke engine operates on these principles, with the rotating shaft causing pressure differences in the oil that "lift" the shaft from contact with the surrounding metal, until pressure (and therefore spacing) is roughly equal on all sides.
A ping-pong ball floating on a column of air self-stabilizes in the same way.)
The primary concern for these turbopumps becomes heat. So heat transfer and temperature of the "lubricating" fluid become more important than its other nominative qualities as a lubricant. Fluids being pumped at cryogenic temperatures can obviously help here.
So instead of a normal "lubricant", most of these turbopump designs just run a portion of the fuel/oxidizer fluid through the critical areas to provide the surface separation and cooling required.