Many of the sources that will help locate details of the family are only recently online so you (or your friend) are very fortunate.
IGI (
www.familysearch.org) lists 3 of the sons: George (1875), Robert (1876), William (1880)- few Irish births in IGI after 1882 so that's why John isn't listed.
1911 census for Co. Antrim and Co, Down just put online the end of December. See here to search:
www.census.nationalarchives.ie/searchEven more recent is indexes to Irish BMD on LDS Pilot site. There is a death for a Robert Lemon whose death was registered July/Sept.1908. He was 63 years old (born c1845) but registration of births only started 1864 so there will be no birth certificate for him.
The marriage certificate for Robert and Eliza should list their father's names and occupations.
You should be able to get registration districts, volume and page numbers on the site to order certificate.
http://pilot.familysearch.org/recordsearch/start.html#p=2;t=searchable;c=1408347Also, a word of warning- the surname Lemon could have numerous other spellings like Lamont, Lemond, etc.