Enniskillen is the Poor Law Union or later the Civil Registration District
In 1862 the Griffith Valuation took place in Fermanagh. Your William would be about 11.www.askaboutireland.ie
Thomas Walmsley, Parish Killesher, Townland Correen and Poor Law Union Enniskillen
tenant Simpson H. Brereton
#1 Thomas Walmsley bog and turbary 19 acres 1 rood 5 perches
#2Aa house, outbuildings and land 25.3.35
#2B land 3.1.34
Also in this Parish and townland is:
#3 Edward Walmsley, house, outbuilding and land 26.0.35
#4a Edward Walmsley Jr. house, outbuilding and land 44.2.35
Alexander Mills, Parish Inishmacsaint, Townland Ardees Upper, PLU Ballyshannon
tenant of Marq. Ely
#4a house, outbuildings and land 51.1.10
also sharing 4b - free (doesn't indicate if land or how much)
#5 Earls of Summerville, same info as above, herd's house and land 404.3.34
Usually marriages took place in the bride's parish.
If William Walmsley leased the Derrygonnelly pub, he is not in the Commercial Directories
1894 Rev. Walmsley, Lisbellow, Wesleyn (he is the only Walmsley in the directories)
The Derrygonnelly pub didn't exist on Main Street, Parish Inishmacsaint, PLU Enniskillen in 1862
There were 2 forges, a dispenseery, court house, school, police barracks and a flax mill.
However, at this time, liquor could be sold in grocery stores or out of your house, but no Walmsley's.
Fermanagh has parish records at www.rootsireland.ie
- pay website
The current british telephone book shows all 3 names in or around Enniskillen
Walmsley 2 Enniskillen; 1 Clontycoora, Lisbellaw; 1 Skea, Enniskillen;
Mills: Cullen, Enniskillen; Drumgay; Drumlyon; Laragh, Ballyinamallard
Sommerville: 1 Snow Hl, Lisbellaw
Your William was not in the UK 1871 Census. although there is a William from Co. Cork, this census identifies Irish born only.
Looked at 1881 & 1891 but so many William Wamsley's in Lancashire (79) about age 30, its amazing but none Liverpool specifically but you have all that information anyway.
Wished I could of helped more. There are books available at Enneclan that might provide you with background information on conditions in the 1850's, the middle of the Great Famine. I don't think the Sommerville's would be suffering. You might find them on www.landedestates.ie