... How were you able to arrive @ the mothers name for the baptisms? ... Is there any marriage showing for Timothy & Hanora?
It doesn't seem to be widely known but once you are reduced down to a single match on a baptism in the RootsIreland website search index, you can start to put in guesses in the mother's or father's first name, a letter at a time (it's like an inbuilt "starts with" function).
So for example, in addressing your OP about finding Timothy's first marriage or births of children Timothy, John & Hanora, I first searched for children of approximately the right 'age' with a father called Timothy. Then I reduced the options down to a single match (take son Timothy for example, once I had identified a suitable son Timothy in 1879, I narrowed down the date in the search to 1879 so that the search only brings back one match). It is at that point you can start guessing the mother's first name, I usually start with the first letter of any suspicions I have, but if I don't have a clue, I just put in the letter "a" and see if I still get the single match, if not I put in the letter "b" and see if I still get the single match, and so on. In the case of Timothy's baptism in 1879, the single match disappeared when I tried letters "a" though "i", then reappeared when I tried "j", so I knew her name started with "j". Next letter had to be a vowel, "ja", "je", and "ji" caused the single match to disappear again, but "jo" brought it back again. By the time you get a few letters in, you can pretty well guess the name and try it to see if the single match still comes back. It sounds more complicated than it is, once you've done it several times it isn't. In baptism records it only works on first names, not surnames (surnames have to be 100% correct in full). However, in the example I've given, once I knew Timothy junior's mother was Johanna, I went searching for a marriage of Timothy the father to a Johanna, once I found the marriage to Johanna McCarthy, I was able to go back again to the Timothy junior baptism and put in the full mother's name Johanna McCarthy and the 1879 match for him came back, so that's how I knew.
BTW, the only church marriage I can see is a Timothy Lucy to Hanora Harrington in 1843 in Kilnamartyra RC parish.