The placename for the birth of Francis Lally is definitely Westport.
I checked the original parish registers for a record of his baptism on or around Aug. 15 1848 but I did not find it. However the page does state that the baptisms are not in order so the record may be in there somewhere.
This is the link to the original registers for Aughaval/Westport. You should probably go through it yourself and see if you can spot the record. Do bear in mind that, at the time, it would have been pretty unusual for somebody to know their exact date of birth so the date noted in the bible could be out by weeks, months or even years.
You could also search for a marriage record for Thomas and Mary. Traditionally, a couple would marry in the bride's parish so if Mary was not from Westport parish you may not find a record.
The only real source of records for most people for that time period is the parish registers so if there is anything to find, you will find it in there.
Belfast is most definitely not in Co. Mayo. I'm not sure where you mean when you ask about Belsfarsad.