Wexford Town Church and Cemeteries

At the time of James' baptism the Franciscan chapel was used as the main Catholic church, this is appropriately located on Francis street in Wexford town. The Friary was built in the 1820s and is still there, so likely the chapel dates from around the same timeframe. Not long after your James was born the new twin churches were built in Wexford - both quite close to the Friary Church.

Are you certain about the date and place of James' baptism ?
I see a number of baptisms for a James Lambert in Co. Wexford including several in Wexford town, but none in 1844. Do you know parents names for your James ?

The situation regarding Catholic burials is not as straightforward at that time as many Catholic Churches, particularly those in cities and towns did not have attached graveyards. There were several old graveyards in the town which would have been associated with Church of ireland church, e.g. St. Patrick's and St. Mary's near the Friary Church. Some of these would likely be pre-reformation in origin so could have had burial rights for anyone on the parish (not just Church of Ireland). Some registers for these survive and have been scanned by Wexford County Archive. There's also a large Crosstown/St. Ibar's cemetery located on the other side of the River Slaney at Crosstown. Wexford County Archive also hold some burial registers not currently online, including records for Crosstown cemetery.

Thanks for the quick and thorough reply.  James was bptised on November 9, 1844 in Wexford Town (his surname is given as Lamport in the parish record).  His parents were James Lambert and Margaret Wickham.(married December 1, 1838). 

Well done finding that baptism, I managed to miss that as a variation. FMP have transcribed and indexed that baptism as Lampert, which is what the surname looks like to me on the register.

Hope your plans for a trip to Wexford work out - if so enjoy your trip!