Ballindoo or Doocastle was a townland in Costello Barony, in the civil Parish of Kilturra and the Poor Law Union of Swinford. (List of Townlands in Mayo, Wikipedia). I don't know about Lughoon. I tried variations of spelling but nothing matched. I thought it may have been Lough****.
Is the document connected with a pension application? As Irish birth registration only began in 1860s, people who were born before then had to prove their age some other way when applying for a pension, e.g. if they were on 1841 or '51 Irish census. Applicants had to remember where they were at the time of the census, which may have been 50 or 60 years previously, perhaps when they were children. They might have emigrated since; other family members may have been dead or abroad, so it's not surprising they couldn't remember every detail. Add to that, loss of Census records.