I have hit a brick wall

[Squirrelly]

Thank you - I will look into that. 

[Ladyhawk]

Does anyone know if there are records showing whether Thomas Edward Williams died in the hospital or perhaps the dates he was admitted/discharged please? 

That may help me find him.  Thank you.

Not that this answers your question but The hospital had its origins in the Southern and Toxteth Hospital in Greenland Street which opened in January 1842.
A concert given by Jenny Lind allowed an extra floor to be added to the building in the 1850s, shortly before it became the Southern Hospital in 1857.

I don’t know if you will find anything useful on this link

Records of the Royal Southern Hospital, Liverpool Hospital for Consumption and Diseases of the Chest
https://discovery.nationalarchives.gov.uk/details/r/c3279399-8fc0-4cb6-a872-f76540cd67fa - records are at Liverpool Record Office

For info. and anyone else looking  I've added the 1871 census details for Thomas

Thomas E Williams Age: 16, occupation Rigger
Relation:   Patient
Where born:   Liverpool, Lancashire
Southern Hospital Liverpool
Piece:   3778
Folio:   163
Page number:   3

[Squirrelly]

Thank you. I will have a look

[Radcliff]

St Peter Liverpool,
Alfreda Williams
born 1st Jan 1879,
baptised 29th Jan,
abode Walton,

father David Williams a book keeper mother Jane,