Have found the notes I had on Walter Crossley but it may not be any more than you already have by now but will post here to save others looking up the same information.
William CROSSLEY (born c1855 Belfast) m.1 Helen SHAW.
In 1881 they are living at Newton, Renfrew., Scotland: William Crossley 26 Ireland lithographer, wife Helen Crossley 26 Airdrie Lanark, dau. Elizabeth Crossley 5 Renfrew., son William Crossley 4 Renfrew., son Thomas Crossly 2 Renfrew.
William Crossley m.2 (2 Jan.1889- info. given above) Martha PRINGLE (born c1870 Co.Cavan, died 1916 Belfast). Three children from this marriage: John (c1891), Kathleen (1902) and child d.before 1911. 1911 census William, lithographer, and family living at Lismain St.
William CROSSLEY (born c1877 Renfrew.), son of William & Helen, m.(1904 Belfast) Margaret Jane Thompson (born c1873 Belfast). 1911 census William Crossley, lithographic printer, living at Ardgowan St. with wife Margaret Jane and 4 children (2 died before 1911): Georgina Thompson (born 1905), Elizabeth Tate (born 1907), William (born c1908), Thomas (born 1910).
Thomas CROSSLEY (born c1879 Renfrew.), another son of William & Helen, m.(1905) Anne/Annie. 1911 census living Roselyn St. with 3 daughters: Ella [Ellen Shaw born 1906], Annie [born 1907?], Emma [Emily born 1910?].
Elizabeth "Lizzie" CROSSLEY (born c1876 Renfrew.), dau. of William & Helen, m.(31 Aug.190 Belfast- info. given above) David Henry Tate. 1911 census living London Road with their 4 children: David Henry (1902), William George (c1903), Maude (c1907), Eliza Jane (c1915). Also in the household is Walter Crossley 'relative' age 18 machine boy born U.S.
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