Have you found her on a census?
Do you know the name of her order at Sacred Heart Convent and what kind of order it was e.g. teaching, nursing? Was it a missionary order i.e. was she likely to have worked abroad and possibly died in a foreign country?
Diocesan almanacs/directories were published. They contained information about Catholic establishments. I think they contained lists of clergy who had died since the previous publication but I don't know if lists of deceased nuns were included. There are some old directories online. Liverpool is an arch-diocese.
Possible obituary sources: Local newspapers; national Catholic press: e.g. "The Universe", "The Tablet" (there were others); there may have been a more local Catholic newspaper, in view of the large R.C. population in Liverpool and Lancashire. There are some Catholic papers on Find My Past.
Catholic Family History Society has a publications list, a blog, website, &c. One publication is "Who were the Nuns" but I think nuns in it were too early for your lady. I suggest you look at the Catholic FHS as that is the specialist FH society and a lot of members are either based in NW England or had ancestors from there.
It's difficult as it's a wide span of years to search and she had a common surname.
Also Liverpool/Merseyside-based FH groups.
