Generally caused by oil in the diff with no/knackered friction modifiers.
Or wear in the plates, however first port of cal is change the oil and make sure you fill it with LSD specific!! wont feel the difference straight away but after a few hundred the diff will start to work properly again assuming the plates are ok!!! 
I got it from another forum member with the axles removed and the drive shafft ground off leving a stub of 10cm of drive shaft.
That left me reassured that it probably came from a car that was disassembled for reasons othr than a faulty differential.
It sat on its side in a suitcase in my garage for 3 months and a fair amount of oil did drain out.
I've just had it fitted and the oil added is the right oil for LSD. I "hope" that they have added enough oild (1 litre), and not too much.
I'm gathering small hope from the highlighted text above that there is a chance that it settles down over the next few hundred miles or so.
I must admit if you are very delicate with your right foot at low speeds it can be "worked around" i.e. you can avoid the mild thump, but it does thump slightly (and unavoidably) when you 1st engage the car into drive from neutral.
Any comments? Am I on a reasonable tack here with this hope?