For everyone who experiences this noise and has it quieted with a diff fluid additive, don't be surprised if the noise comes back. To some extent, it is the clutch packs in the LSD doing what they are designed to do. The noise is not indicative of any damage being done, and you can ignore it indefinitely.
Many will never hear it because they don't routinely make prolonged tight turns at low speeds (e.g. looping up or down in a multi-deck parking garage or as in the diagram above).
This noise is relatively common in all autos equipped with LSD and large tires. The LSD clutch packs are there to allow the inner tire to barely rotate, while the outer tire is rotating at a much greater relative rate. In tight turns at higher speeds, the relative difference in wheel rotation between inner and outer tires is minimal.