You need to buy your grandmother's birth cert. from the GRO, London [which can now be done over the Internet]. The index ref. can be seen on the old St Cath's House films which are widely available here in Oz, at family history societies, etc. With her name, a rough date of birth, and the area code for Salford [ask for this at the FHS], it doesn't take long to go through the quarters to find possible entries. The birth cert. will give her father's name and occupation, name and maiden surname of the mother, as well as addresses and informant. Try for a sibling if there are too many Lilians. You can order the 1891 census on film through a local LDS centre when you have an address, and with luck that will give exact places of birth for the parents plus a lot of other details.
Sue