what religious denomination and timeframe ?
most of the city graveyards were closed during the 19th century and burials usually took place in one of the larger cemeteries on the outskirts of the city, e.g. Glasnevin, Mount Jerome or a little later Deansgrange, or sometimes in a plot outside Dublin if the family originated outside the city, or county... if not too far away. Burial records for Deansgrange are available free online, Glasnevin records are on a paywebsite, there are also various Headstone transcripts on line, e.g. IGP, FindAGrave etc
You can see a map of the various graveyards & cemeteries in Dublin county and city with details on any records on the
Dublin City Library website also a
map hereLime street was in St. Mark's civil and church of Ireland parish, the church was on Great Brunswick Street, and has an attached graveyard, the church building and graveyard are still there although not functioning as a church. The graveyard may at times have been shared with other denominations, e.g. RC Presbyterian etc, living in the same parish although these may not have been included in the burial registers.