On top of the evidence indicating the connection between William King Lynar, Eliza Glover, and the children Alfred, Olivia Jane and Jonathon Joseph, here are another couple of references that corroborate the sibling relationship between the two surviving children Alfred and Olivia Jane and suggest continuing contact between the respective families years later. The first reference is the death notice for Alfred in the Belfast Telegraph of 13 August 1923:
LYNER - August 12, 1923, at his residence, 26 Flora Street, Alfred, the dearly loved and loving husband of Martha Lyner. His remains will be removed from the above address for interment in Dundonald Cemetery, on Tuesday, the 14th inst., at 2.30 p.m. "Safe in the arms of Jesus." Deeply regretted by his sorrowing Wife and Sons, Daughters-in-law, and Grandchildren, also Sister and Brother-in-law and Nephew. MARTHA LYNER.
So as well as Alfred's own family, the only other relations getting a mention were a "Sister and Brother-in-law and Nephew", a description that is consistent with the only other relatives we have evidence of in this story so far, namely Olivia and Edmund Costley whose only child was a son - William John - and therefore a nephew to Alfred. It would have been nice if the Costleys had actually been named, still, from the way its written I'm pretty confident that it's them.
The second reference relates to Alfred's son Edward. The Belfast Newsletter of 25 November 1914 reported the death of Edward Lynar from his war wounds and said that he "was a member of Roe Memorial Total Abstinence L.O.L. 938, Ballymacarrett". Working back from that, on 25 February 1911, the Belfast Weekly Telegraph reported on a social evening held by the Roe Memorial L.O.L. No. 938, at which one of the ladies mentioned as presiding at the tea tables was a Mrs. Costley. There was also mention of a Br. Edward Lyner contributing to the programme (of entertainment) and a Br. Edmund Costley being the Secretary of the Lodge. The same newspaper of 16 February 1911, covering a reunion of members of the Roe Memorial L.O.L. 938, named the secretary as Br. Edmund J. Costley and mentioned that Br. Edward Lyner provided a recitation as part of the musical programme.
Now if these were run-of-the-mill names, it would be no great deal, but given how VERY rare - if not unique - these specific forename/surname combinations were (as can be verified by the 1911 Ireland census), I think it is way beyond mere co-incidence that they should appear together in the one context and to me it indicates the probability that Olivia Jane Costley's family and Alfred Lynar's family knew each other and occasionally interacted/associated.