It depends on the type of Limited Slip Differential (LSD). The “plate” or “Salisbury” type of LSD uses small clutch plates each side of the differential. These need a special
Limited Slip oil, which contains friction modifiers to reduce squeal and provide smooth power take up. Suitable Millers gear oils have LS in their name. The cam and pawl and torque-biasing differentials do not need an LS oil, just a very good performance gear oil, although there is no harm to be done in running these types on LS oil.
You can find details of the Millers LS gear oils by clicking on the following links:
However, there are some exceptions to these guidelines. Unfortunately synchromesh does not like friction modifiers. They make it slip when it is trying to grip, and could cause the gear change to become difficult. Hence a problem arises in some front wheel drive cars where the synchromesh gearbox shares the same oil as a plate type LSD. Millers CRX 75w90 NT fully synthetic competition gear oil is the best compromise, as it has been formulated with this situation in mind.