Hi,
I just came across this post now and might have some useful info for you. I hope the info will help you to understand the layout of the city and save you a lot of confusion over names and locations.
1 The Richmond Lunatic Asylum was located in Grangegorman Parish on the north side of Dublin city and was known to Dubliners for years simply as Grangegorman. This was in Arran Quay Ward or administrative boundary. During the First World War part of the asylum was used by the military to treat soldiers affected by shell-shock and gas attacks.
I read somewhere (cannot remember where) that research and studies were carried out on the soldiers to understand the effects of mustard gas on the human nervous system and how to better protect soldiers from future attacks. Also, that a lot of soldiers from other parts of Britain were kept here for a long time as the army authorities didn't want them to terrify the public and affect recruitment and voting. Further to this, I also heard that a lot of soldiers suffering from shell-shock and mustard gas were posted as missing in action and lived out the remainder of their lives in Ireland without their families knowing if they were dead or alive.
2 The Richmond Female Penitentiary (prison) was located just to the north of the asylum in the same district (see picture of map). Both of the above establishments were close to the North Circular road and Royal Canal.
3 The Richmond Male Penitentiary was located between the South Circular Road and the Grand Canal on the south side of the city near the junction of Clanbrasil Street.
The asylum board of governors changed it's name in the late 19th century to the Richmond District Lunatic Asylum. The word "district" here does not mean that Richmond was a district in it's own right but refers to all of North Dublin city and parts of the county.
Both prisons were designed by the architect Francis Johnston and the street view of both main blocks look identical but the interior layout and amount of buildings differed greatly. This may be due to the amount of ground available on which to build each prison, again, see the map pictures.
On the north side, the female prison was closed a long time ago due to transportation of convicts to Australia and subsequent falling numbers in inmates and it lay disused and empty for a long time. It was reduced to a ruinous state by severe vandalism in recent years with the interiors gutted of all fixtures and fittings and was eventually partly demolished for safety reasons. All that remains is the main block which I believe is now part of Dublin City University IT campus.
On the south side, the male prison was known both as the Richmond Male Penitentiary and, the Richmond Bridewell and is shown as such on maps of different years. It was also colloquially known as the "Cease To Do Evil Hotel" from an inscription over the main gate which read "Cease To Do Evil, Learn To Do Good" which was meant to give the impression that if convicts become model prisoners they will earn their freedom.
Around 1893 this prison closed down and was sold to the War department and converted to a military barracks known as Wellington Barracks. I say military barracks as distinct from police barracks which we had in Ireland at that time.
in 1922 it was handed over to the new Irish Free State Army and was soon afterwards renamed Griffith Barracks which remained in use up until 1998 when the last remaining military units moved out to take up residence in other barracks around the city. In 1991 it was put up for auction and bought by a consortium for conversion into a College campus known today as Griffith College Dublin. Incidentally, I served in the Irish army and was stationed in Griffith barracks for 14 years and took part in the closing ceremony of the last units to move out in 1988.
I suggest you make a search on Google images and Google Earth (or maps) for Grangegorman and Griffith College
I hope this helps to make your search easier and clears up any confusion over names and locations.
Best of luck with your research.
P.S. apologies about the quality of the picture. I meant to post several pictures but had difficulty loading them.