If you have access to Ancestry, either via a subscription or at your local library, I'd advise searching the cemetery records.
Ancestry have a database called England & Scotland, Select Cemetery Registers, 1800-2016. This includes various cemeteries in the Liverpool area.
Also try the following (also on Ancestry):
Liverpool, England, Church of England Burials, 1813-1975 and /or
Liverpool, England, Catholic Burials, 1813-1985
Search using his name and the year of death and, fingers crossed, you may find his entry in one of the above databases.
Good luck with it
Boo