Hi RosniakYou have ever good reason to connect Thomas McAlister a weaver to the Thomas listed in the 1819 Lisburn directory who was living at Johnston's Entry.]
BUT how do you know he was in Smithfield?I rechecked and found spelling variations and another of later interest perhaps
1819 Lisburn section DIRECTORY OF LISBURN for 1819
McCallister, Eliza, haberdasher, Castle Street
McCallister, John, nailer, Antrim Lane
McCallister, Catharine, Antrim Lane
McCallister, Alexander, coal porter, Antrim Lane
McCallister, Thomas, weaver, Johnson's EntryMcCallister, Neesy, nailer, Smithfield
McCallister, Charles, servant, Bridge End
McCallister, James, knit shoe maker, Bridge Street
Morgan, Hugh, weaver, Bridge End whose family continued in lisburn
in the same directory
Trades and Professions in Lisburn
Haberdashers
McCalister, Eliza, Castle Street
A Source I use regularly but with caution
1823-1837 Tithes Applotment Books based upon the index work of the Irish Genealogy Hub’s listing for each parish in Northern Ireland, which are quicker to lookup if you know the parish! The relevant original books are in the Public Record Office of Northern Ireland (PRONI) Belfast. The entry is a simple one liner The result was unexpected because
the tithes for Blaris are minimal, so that looks like Lisburn was protected by the Church of Ireland who was collecting the Tithes
McAllister, Charles-Townland: Largymore Year: 1834-Blaris-Antrim
McAllister, Charles-Townland: Largymore Year: 1834-Blaris-Down & Antrim----
Largymore is to the west side of Blaris and may not be useful
Ancestryireland has a couple of births
Thomas McCalister 1818 father Thomas Antrim
Margaret Mccalister 1834 father Thomas Antrim
Some street directories
1850 New Commercial Directory Lisburn section see PRONI I couldn’t find any name relevant quickly
1852 street directory see
http://www.lennonwylie.co.uk/1852PD3.htmMcCalister, Thomas, tailor, Castle Street [connection?]
Morgan, George, weaver, Bridge Street [connection?]
Murphy, Patrick, grocer and publican, Bow Street [connection?]
street directory 1861 lennonwylie has
Walker, John, confectioner, 61 Donegall Street.
Walker, John, grocer, 37 Union Street.
street directory 1877 lennonwylie has
Walker, John, mechanic, 290 Conway Street
Walker, John, spirit dealer and oyster house, 10, 8 & 7 Winecellar Entry
Walker, John, shoe maker, 124 Old Lodge Road
Walker, John, grocer, 101 Old Lodge Road
Walker, John, confectioner and pastry baker, 75 Donegall Street
Walker, John, traveller, 73 Belvoir Place, New Ball
Mary McAlister (1835) Lisburn Cathedral.A Mary McAlister was living at Antrim St lisnagarvy in 1862 Griffiths valuation; As was an Alexander McAlister in separate property
Your very useful children list to which I add minor possible extras
Ann McAlister (b 1823) Lisburn Cathedral. married George Morgan, moved to Belfast, died 1886, buried City Cemetery. No George in 1861 belfast Directory or 1877
William McAlister (1826) Lisburn Cathedral. could be McAlister, William, boot and shoe maker, 23 & 61 North Street
Joseph McAlister (1829) Lisburn Cathedral.married Catherine Murphy in Belfast in 1849, no further knowledge.confirmed [1849 see ancestryireland.com] could he be 1877 street directory McAlister, J., spirit dealer, 147 & 149 McAlister Buildings, Grosvenor Street or McCallister, J., bookkeeper, 21 Ormeau Street
Harriett McAlister (1834) place? Co Antrim married [1851 see ancestryireland.com] John Walker, moved to Belfast, had three children in 1858, 1861 & 1863. [source?}
street directory 1861 lennonwylie has
Walker, John, confectioner, 61 Donegall Street.
Walker, John, grocer, 37 Union Street.
street directory 1877 lennonwylie has
Walker, John, mechanic, 290 Conway Street
Walker, John, spirit dealer and oyster house, 10, 8 & 7 Winecellar Entry
Walker, John, shoe maker, 124 Old Lodge Road
Walker, John, grocer, 101 Old Lodge Road
Walker, John, confectioner and pastry baker, 75 Donegall Street
Walker, John, traveller, 73 Belvoir Place, New Ball
Mary McAlister (1835) Lisburn Cathedral.A Mary McAlister was living at Antrim St lisnagarvy in 1862 Griffiths valuation; As was an Alexander McAlister in separate property
could they have had more childrensee
www.ancestryireland.com has a couple of possible births
Thomas McCalister 1818 father Thomas Antrim
Margaret Mccalister 1834 father Thomas Antrim
You mentioned
Thomas Abbot & Mary McAlister lived at Smithfield in 1834 when they had a daughter Elizabeth. This Elizabeth is not listed in ancestryireland under births inc McCalister
Alexander & Jane McAlister lived at Smithfield in 1827 when they had a daughter Catherine. This Catherine is not listed in ancestryireland under births inc McCalister
Good Luck onwards