I search the IFHF database at rootsireland.ie. It has 19 million B/M/D records. The database isn't complete yet, but DOES include Co. Tipperary, and the surname Lamb.
For Mary (but not Maria) Lamb, B 1829 +/- 1 yr, Co. Tipperary, I found 2 B records. However, neither has a mother named Carrie.
Carrie is an unusual forename in Ireland. This is the first time I have seen it in several years of research. Are you certain it wasn't a nickname. I also couldn't find it anywhere else in Ireland with the surname Lamb.
For a Marriage to Jeremiah Dillon, I found 0 M records at any date, anywhere in the existing database.
Suggest you go to the rootsireland.ie website, register (free), and wait until more records are added.