The short answer is yes, you can use Lucas in your differential. The long answer is a bit more complicated.
Lucas oil is a petroleum-based product manufactured by the Lucas Oil Company. It is marketed as a preventative maintenance and break-in additive for differentials and other automotive applications.
Lucas oil products are not compatible with all fluids. For example, they should not be mixed with synthetic oils or Eaton fluids. Additionally, using Lucas oil in an application that does not recommend it could void your warranty.
If you do decide to use Lucas oil in your differential, be sure to follow the directions on the bottle. Over-diluting the product can actually reduce its effectiveness.