Julie,on rootsireland.ie which is a pay per view site I found only 1 birth for Peter Lynch in 1759 co Westmeath.The only thing is the father's name Peter doesn't come up on this record. It also has several deaths for Peter Lynch Sr: co Meath 1832,1839,1840 co Westmeath 1827 co Offaly 1827 Again no way to know if any or none are the man you seek.
Lastly,found this marriage on familysearch.org:
groom:Peter Lynch bride:Ann Lynch date of marriage:27 October 1758 place of marriage:Saint John,Limerick,co Limerick
You would have to research further to see if any of these may pertain to your family,Kim