I hope you don't mind me replying to this thread.
Michael Joseph Bulger was the main mover about creating London Irish Rugby Football Club, chairing the initial meeting when talks about starting the club took place in Chancery Lane in March 1898. Lawrence and Michael both played for the club, with Lawrence joining the club in 1899 (it's second season).
The news of Lawrence's death was from the Irish Independent:
March 20 1928, Irish Independent, Dr. Laurence Bulger, an old Irish International Rugby player, collapsed and died while leaving Twickenham just before the England v. Scotland match began on Saturday. When his playing days were over, Dr. Bulger acted in an hon. medical capacity to the players at Twickenham. He leaves a grown-up son and daughter.
"March 21 1928, Irish Independent, Irish Rugby International. The sudden death of Dr. Lawrence Quinlivan Bulger, the old Irish International Rugby player, after leaving the Twickenham ground prior to the start of Saturday's International match, has been learned of with deep regret in sporting circles and amongst his compatriots in London. Dr Bulger was the son of the late Mrs. Bulger, of Thomond House, Lisdoonvarna, but his family was known in Dublin. In the nineties the name of "Larry" Bulger was a household word in Irish football circles. He played as a school-boy for the Lansdowne Club, and went to South Africa in 1896 on a football tour. Dr. Bulger practised for many years at Twickenham where he was physician to ex-king Manoel of Portugal and his wife. For some time he resided at Pinner, where the funeral will take place at 12 o'clock tomorrow. The service in the church and at the graveside will be conducted by Father John Caulfield, parish priest of Pinner.
March 23 1928, Irish Independent, DR. BULGER'S FUNERAL. The funeral of the late Dr. Lawrence Quinlivan Bulger, the old Irish Rugby International took place yesterday at Pinner Cemetery, says our London Correspondent. Many of his friends were present, amonst them being Sir Thomas Moloney, formerly Lord Chief Justice of Ireland, who was accompanied by his daughter. Father John Caulfield celebrated a Mass of Requiem, and officated said:- "We are burying a man who was a God-fearing Christian, who reflected in his daily life the Gospel teaching. As his parish priest I have no hesitation in saying that he was a model which each of us might well copy". Many beautiful wreaths from Irish and other friends were laid on the grave.
And the Times The Times Wednesday March 21, 1928. LAWRENCE QUINLIVAN (LARRY), dearly beloved husband of MARIE QUINLIVAN BULGER (nee Tinchant), of Fairholme, Hatch End, son of the late Mr. and Mrs. D.S. Bulger, of Lisdoonvarna, Co. Limerick. Funeral at the Convert of Our Lady of Lourdes, Hatch End, Middlesex, tomorrow (Thursday), at 11 am. R.I.P.
At some time Lawrence had the following addresses in what is now London: 688 Romford Road, Essex (which is in Wanstead) and Poplar Lodge, Twickenham, Middlesex.
From what I can tell Lawrences son was Marcel Lawrence Droubaix Quinlivan Bulger (there is a medal card available for him) giving the address of Poplar Lodge.