I live in Melbourne and we still have a few LSS (although we have lost a few recently), but as mentioned they are generally out in the suburbs.
If you're in the eastern suburbs at all, I can highly recommend
Bellbird Paperarts in Blackburn South. Cathy who owns the store can make amazing recommendations on paper, inks, etc.
Creative Dreams in Boronia (also eastern suburbs) is also a great local store.
Kaisercraft also have their own outlet stores in some suburban shopping centres (and one near Southern Cross Station in the city) and sell a lot of their retired stock very cheaply. The Melbourne stores are: Spencer (Southern Cross Station outlets); Bayside (Frankston); Moorabbin DFO; Point Cook; The Glen (Glen Waverley); University Hill (Bundoora) and The Well (Camberwell). A full list of the addresses is on the Outlets tab
on this webpage.
Hope this is useful!