Hi,
The Brindle Workhouse closed the year after the 1871 Census, Christmas 1872, so if he was still there then, he probably was transferred to the, then new, Eaves Lane workhouse in Chorley, where all the inmates moved to. It may be worth looking with that address for a death record and/or in a later Census - 1881 etc. as they may say more than just Ireland.
From my own researches on other things I know it's almost impossible to trace births etc. in Ireland unless you have some sort of locality to go on. (As most central records were destroyed in the 'troubles' - though the local copies are still in the parishes.) The Lancashire Family History & Heraldry Society have an Irish Branch that are very well informed and helpful. They even have their own library. See their website
http://www.lfhhs.org.uk/irish/index.htmFailing that, best I can suggest, if you haven't already tried is to look at the scan of the actual census return rather than the transcript. Sometimes there's more detail on the form itself - I'll check my copy and get back to you if there is more than Ireland mentioned. Only other thing I can think of might be to ask at the nearest Catholic Church if they've any record - St Joseph's Benedictine 'Mission',
http://www.brindlestjosephs.org.uk/ I know they dealt with the workhouse catholic inmates.
Sorry couldn't be more definite, hope this helps,
Bernard