There is no real need to lube the shengshou 4x4 V3. But the last time I took it apart I used a little ammount of lube in the internal pieces and in one of each edge pieces and now it turns really good (After a few solves), using differential oil. I also adjusted the tension screwing it all in and then loosening it a few (Less than 1/4 I thing, but I am not sure). Just try until you get the tension you like. But don't loosen it too much or it will pop on every solve.
I mean that you can lube it if you want, but don't expect it to be any better.