Hello, I am familiar with the Denzilles Lane area having worked nearby for over 10 years, I have no family information but had a strange coincidence this morning while out was talking to a man whose family were from there, he was not aware of your family but attended the school and church in Westland Row (area nearby were Pearse Station, railway is).
In 1963 there was a tenement collapse in Fenian Street, Denzilles Lane runs behind Fenian street, there were 9 deaths including 2 children, if you search online you will see some info on it. This was one of a number of such collapses in Dublin, there was an outcry and people were moved out of the city centre to new houses outside the city (then but not now outside) apparently the man told me people from Denzilles Lane were moved to the Milltown / Churchtown area of Dublin (they adjoin but those names occur in other parts of Ireland too).
An email to Pearse Street library may assist with more information (main Dublin library for genealogy) https://www.dublincity.ie/dublin-city-library-archive this is actually close to the area too.
The name Lynch is common enough, did you know Eliza Lynch is the symbol of Paraguay, there is a radio documentary on it if interested but she was from Cork. The other name Fullam is less common and the man told me there were a Fullam family in the area circa 1960 but not on the lane where he remembers the people fondly. There was a well know soccer player in the late 1960s early 1970s called Johnny Fullam, played mainly for Shamrock Rovers, they were then based in Milltown, there was another soccer player also named Bunny Fullam, around 1960 and you can Google them both.
Hopefully someone will come along with more information.
Good Luck
Pat