Lathe Chuck Grease

The schunk grease has 40-50% limestone in it. I've never seen a grease with that in it but I assume it must be used a solid lubricant. It otherwise appears to be a pretty standard Li-12 grease.

The chuck-eez has a dose of molybdenum disulfide in it. Moly is another solid lubricant.

Didn't really find any info on the k05.

Basically they are all tacky water resistant greases with a healthy dose of solid lubricant in them.

You'll get a dozen different answers as to what the manufacturer recommends vs what other guys are using.
As usual searching the internet gives opposing answers from “any grease works, my shop has done it for decades” to “xxxx grease is the only one that maintains clamping pressure”.
The manufacturer is adamant about using a chuck specific grease but doesn’t specify a brand.
My local supplier carries Chuck-eez.