I searched the Irish Family History Foundation's online database at ROOTSIRELAND.IE. It has abt 20 M B/M/D, civil, census, etc records for most Irish counties. Records before 1863 are increasingly scarce - and almost non-existant before 1800.
For LILLY Lernan B 1889 +/- 3 yrs, Co. Longford, with a father forenamed William and mother Julia, I found 1 B record in 1889.
For Agnes Lernan/Lerhinan B 1895 +/- 3 yrs, ditto, I found 0 records.
For a William Lernan/Lerhinan and Julia Anderton marriage at any date, anywhere in Ireland, I found 0 records.