Sure thing you can fit lsds in the gearbox. the starlet came from factory with gearbox lsd thats outside the gearbox,hence the different bell housing and length of drive shafts. There are two types of lsds that you can fit in the normal gearbox,Mechanical or Helical type.
Both are equally good,one needs repair after sometime [ Mechanical/clutch type] and the other one [Helical] is fit and forget.
Over here most people go for Quaife/TRD/Kaaz. So it up to you.At the moment there is a great deal on one lsd in the sale section. TRD lsd for around 400 bucks and the seller is a nice chap too [ bought from him before ].
I suggest you read a bit on the site,lots of info.
Hope this helps.