Yes, the differentials need a certain amount of torque before they will lock.
Again, without a road test, I would not conclude that the one you have is not a limited slip dif.
Don't get me wrong, but you have wrong thinking of LSD work.
When both wheels are loosen - mechanism is locked & both wheels should spin in the same direction.
In good working diff - for example LSD 25% mean that until torque reach ca. 5mkp (difference between the wheels) - mechanism could not slip.
That's why LSD mechanism have preload/tension springs inside along with dog ears & friction discs, that keep it locked up to specific torque.
That's why when for example there is no grip on the road (rain/snow/sand etc.) both wheels with working LSD will spin in the same direction, same speed, same force & that's why LSD is needed for the drifting.
LSD 40% = ca. 15mkp (force difference between wheels) until one of the wheels start to slip (will start to work as open diff).
LSD 0% = 0 mkp, so no force is needed, that's why it's called open. That mean when there will be any difference in force between wheels, all power immediately will go on the wheel with less grip.
Race/track cars have even higher lock %, because most of time they are on dry high grip asphalt & need higher forces until one of the wheels start the "correction" function.