I’ll be honest though I did know there was a lane beside Centra on D’Olier St, I didn’t know its name or quite how unique it was. Thanks to Pádraig Kelly and hXci for bringing my full attention to it.
Leinster Market is a small, covered lane that links D’Olier Street and Hawkins Street. It was described by in J.T. Gilbert in 1861 as a ‘quaint, narrow old passage, which has very little light even in its open parts, and at either end has to burrow under the first floors of houses that lie right across the way’.

D'Olier St. entrance to Leinster Market. (Photo credit - Matthew S.)

Hawkins St. entrance to Leinster Market. (Photo credit - Matthew S.)
Interior:

Inside view (Picture credit - Brian, Pix.ie)
In the unforgetably named ‘History of the City of Dublin: from the earliest accounts to the present time : containing its annals … to which are added, biographical notices of eminent men … ; in two volumes, illustrated with numerous plates, plans, and maps, Volume 2′ published in 1812:
Leinster Market has been erected within these few years in the vicinity of Carisle Bridge, and leads from Dolier Street to Hawkins Street, through the new buidlings. It is entered by a handsome iron gates, the passages are flagged, and the whole kept perfectly safe and clean. As yet but five of its stalls are occupied for the sale of meat.
On June 09 1953 Miss Bridget Greene an assistant at Skeffington’s confectioner shop in Leinster Market was held up by three youths. One of the gang ‘asked for ice cream’ while another ‘grabbed a mineral water bottle’ and struck her over the head with it ‘in an attempt to reach the till’. Though ‘stunned’, Miss Greene managed to set off a ‘special burglar alarm’ and the youths made off in the direction of Hawkins St. It was reported that this was the third occasion in the last three years in which attempts had been made to rob the till during the day.
On Nov 3 1969, cylinders of gas and drums of diesel oil exploded in a storage building in the alley off Leinster Market. The fire was put out in fifteen minutes.
In 1993, a bronze plaque, of an ‘old guy reading a rumpled up book’, was erected in the lane by the Dublin Literary Pub Crawl to celebrate the characters who use Leinster Market – ‘the gougers, the bus drivers going in for a smoke, and the people walking through’.

Plaque, Leinster Market. (c) Jay Carax
Leinster Market throughout history:

Leinster Market. Late 19th century?

Leinster Market. Early 20th century?
Mapping the lane’s history:

1836

1848

c1907

2011