I have Permanent Residence in UK and would need to travel to Dublin for Business. Do I have to get visa? or can I travel without it? It would only be for 1 day.
As others have said, and you have found out yourself, you do need a visa as a Sri Lankan passport holder, irrespective of what permanent residence permits you hold.
You can do this by visiting this link, reading it, then clicking the 'Apply for a visa' button at the bottom of the page. If you would like to do any further reading in addition to the previous link, you could also have a look at this one.
Hope that helps. Good luck with your application.