Someone told me that this pub is named after 'Lugs' Brannigan. Brannigan was a policeman who had been a boxer and if you were arrested by him it is most likely that at the very least you would have a black eye by the time you arrived at the station.
The nickname 'Lugs' refers to his prominent ears. A keen boxer, he achieved his nickname 'Lugs' early in life due to his Cauliflower ears, a condition most common among amateur wrestlers, rugby players, mixed martial artists and grapplers, it is said he got the name because of his ears by a Dublin criminal in the 1940s - a nickname he disliked. He was known as Jim, "Branno" and "The Bran" to his Garda colleagues.
The people who approved of his policing methods were most likely at the receiving end for example here is a quote from a local politician "There is an onus on us to ensure that the guardians of law and order are protected. We have reached the point where the balance of advantage has been taken from the Gardaí and given to the criminals. As a university student I recall seeing Garda “Lugs” Branigan in the Olympic Ballroom. He parted the hordes like the Dead Sea to take three people who were in front of the band stand into the back alley and rendered his own justice. Nobody protested."