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Records for Kilgass begin in 1825 for RC parish records and 1886 for Church of Ireland Records. As she was born prior to 1864 there will be no birth record for Elizabeth.
I haven't been able to locate any baptism records for any children born to a father William Walker in Co. Sligo. If she was married in Kilglass as your marriage record suggests this is a fairly good indicator of her parish of birth as usually (as is the case now) the couple would have married in the home parish of the bride. That marriage record though, gives her townland as 'Ballygilcash' and that is as close as you can get to a place location in Ireland. Ballygilcash is in the parish of Kilmacshalgan. Francis's townland was Leafonny in the parish of Kilglass.
Using Francis's townland I checked the 1901 Census and located a Grey family with an Eliza aged 73, putting her year of birth as approx 1828 which would fit your details thus far. At that time she was a widow. You can see the entry HERE. She is listed with her son James, two nephews and a boarder. She is listed 10 yeas later in the 1911 Census and one of her grandson's uses 'Walker' as a middle name. So, at least by 1911 you know where they lived. If you go to the Valuation Office you might be able to learn who was in possession of the plot up to the 1960s. The staff in there are very nice and will be able to help you out.
I have three maps below one showing the general area and the other the townland of 'Ballykilcash'. Elizabeth's father was recorded as a farmer on her marriage certificate but the only William recorded in the Griffith's Valuation in that area is in the parish of Easkey, townland of Cooga which is not very far from Ballykilcash. If you can time during your stay you could also visit the Valuation Office to have a look at the Cancelled Books. You can learn about them HERE.
When you come to Ireland you could check out the ED/ (Education) series of files and records in the National Archives. If you know where she taught you might be able to find out more from a salary or pension file. Unfortunately these are not online and you will have to travel to the National Archives in Dublin.
Hope this helps