Hi, just saw your posts and have some information that will most likely assist you both with William and Thomas Lannary.
William and Thomas were indeed the sons of Joseph Lannary and Johannah Mullane.
Joseph was born in Dublin abt 1849 and died at 6 Dunnolly St, Glasgow, Scotland on 15/10/1905.
I have Johannah as being born in Cork (information given to me by another source) abt 1851. She died at age 74 at 11 High St, Kincardine.
Johannah was known as both Hannah and Ann and her maiden name was spelt in various ways ie Mullan, Mullin, Mullen and Mullane.
Johannah's parents were William Mullane and Mary Mullane M.S. Cooney.
Joseph's parents were Thomas Lannary and Helen Lannary M.S. Harrison.
William was born Belfast 17 June 1879.
Thomas was born Belfast 13 May 1877.
Ellen was born 26 Kildare St, Belfast, 2 November 1886.
Patrick was born Limerick No 3, Limerick, 19 February 1871.
I have a little more information on William in that he married Maria Barret on 25 october 1901. I found 2 children who I think was theirs 1902 Bridget and 1906 Francis (dec). I think the children may have been named after her parents (remember seeing something to that effect).
Don't know much about Thomas other than he married Jane Boyton on 1 July 1904.
Hope this makes your searching a little easier.
If you have any information that I could use I would be most grateful.