Don’t Do This
The application of grease inside the driver can cause both the springs and pawls to engage improperly. Improper engagement could cause stress on these parts causing them to bend, break, and possibly chip away at the hub shell’s ratchet ring.
Grease also attracts dirt. Dirt can gum up the works, causing a slow driver. Dirt could also potentially tear up your springs and pawls. Oily lubes also attract dirt, so they should be avoided as well.
Teflon dry-film chain lube is OK to use on your rubber “O”-ring in cases of friction (aka. a slow driver). White Lightning is a very popular brand that’s available at most bike shops.
You can also apply a drop of Teflon dry-film chain lube to your pawls and pawl pockets to ease friction. It applies wet and dries to a thin lubricating film, but use it sparingly, as it will build up over time. Dry Graphite powder is also a great substance to keep your driver running smoothly.
Keeping the internals of your hub dry will also maintain a loud cassette noise when freewheeling. You’ve got to love a loud hub!