L.O.L. 68 is still a very active lodge in Ballinderry District called Roses Lane Ends Temperance.
The lodge was originally known as Ballymaclose L.O.L. 68 and met in Ballymaclose Orange Hall that unfortunately no longer exists. This lodge amalgamated with Ballinderry Peace and Plenty L.O.L. 143 around 1908. A number of lodge members are listed in the book "The Faithful & The True: A History of Orangeism in County Antrim", surnames including Cuddy, Bell, Yarr, Johnson, Stitt and Clenaghan. Unfortuantely no mention of Armstrongs or Maxwells.
I will try and make contact with the current secretary of the lodge and get back to you as soon as possible - to improve the chance of coming across any information, what was your G.Grandfather and G.G.Grandfather's rough birth year and death year?