You could try "A Century of Golf at Lahinch: 1892-1992", by Enda Glynn, published in 1991. There are copies in the Clare Library service. Amazon have it also.
Perhaps you have already seen the article by "History Ireland" on "Golf's Early Days in Ireland". The article contains a nice photo of some Lahinch Golf Club members on the course but no women in the photo. Although it did include a brief history of women golfers in Ireland:
Women golfers
Another early arrival on the Irish golfing scene, Malahide Golf Club, had a very distinguished founder. Nathaniel Hone the Younger was one of Ireland’s leading late nineteenth-century painters. He was also captain of the club from 1892 to 1897, having founded it with his brother-in-law. The Malahide Club illustrates an interesting feature of golf in its formative years: the relative equality between men and women. In Malahide, women paid the same entry fee (£2) and annual subscription (£1).
The early development of women’s golf is highlighted by the fact that the Irish Ladies Golfing Union was founded in 1893, just two years after its male counterpart and in the same year as its English equivalent. Irish women golfers achieved success before their male counterparts. Ireland was represented among the 38 entrants at the first British Ladies Amateur Championship played in 1893. Between 1899 and 1907 two Irish women, May Hezlet and Rhona Adair, won a total of five championships.
There was an earlier discussion on this forum on whether or not Irish women of the 19th and early 20th century attended funerals, so found it very interesting that women had such equal rights on the golf course!