Try Lyness Lambag on Google and familytreemakergenealogy,com
Griffith's Valuations 1863 listed:
Lyness, Lambeg, Lisburn
Daniel, Lambeg North
James, " "
John, " "
John, Lambeg South
In 1856-7 4 Lyness famiies were living in the area.
Esther Lyness, daughter of John "LYNAS" arrived in New York October 1877 aboard the "State of Virginia" Born Jan. 19, 1831 in Lambeg she had a sister Mary. She married Robert Heaney Jan. 19, 1861 in Lambeg and and died Feb. 2, 1917 buried in Rossknowlagh, Co. Donegal. Her mother was of English extraction. Robert Heaney was the son of William, mother Jane Downey. It appeared that she has made an overseas voyage previously, possibly as a child. Lyness is a variant of the more common "Lynas". The Creelman connection can also be found on Google as well as the Ros Davies web site. Griffith's listed Anthony Creelman in Lambeg North and David in Lambeg South. See rootschat.com
Lyness was originally a North of England name.