I know this is a very old post, hoping you are still doing research.
I too have Ireland born family members who left and when to Lanarkshire, Scotland. Your post mentions a Bridget Feeley from Roscommon. This is the suspected origin of my family but this is not confirmed.
William & Thomas Feeley brothers born abt 1838-1846 moved to Lanarkshire, living in both Hamilton, Lanarkshire and Avondale, Strathaven, Lanarkshire by 1861 - 1881. William married, in 1863, Ellen McGovern (Irish born) but raised in the same area, as well as Glasgow, Scotland. It would be amazing to somehow find other Feeley family members that have a known connection to this area and better yet a known birth place in Ireland.
Both brothers immigrated to the United States Thomas prior to 1880 and William & family by 1882. Thomas was living, by 1880 in Bloomington, Illinois with thought to be family with the surname of Brennan. This family was from Roscommon.
Anything you could shed on Roscommon / Feeley connection, as well as Lanark Scotland would be greatly appreciated.