i dont think you need both...locking nut and locking tuners. A few folks here have suggested that you can use a locking nut with cheap tuners or just use a good set of locking tuners and a graphite or roller nut.
He answered your question anyway. You don't need both. BTW I read your post wrong too (a minus and a hyphen look the same) With a Floyd I would personally go for a locking nut over locking tuners, that is if I didn't go for both. Locking tuners speed up string changes though so I guess it's down to personal priorities...Welcome to the board