The church itself was built in 1754 (consecrated 1755), when Lancaster's thriving port and expanding population justified an additional place of worship. The tower was added some years later, in 1784, and also used local sandstone from what is now Williamson Park.
Personally, I think Thomas Harrison, the tower's architect, overdid the mix of Georgian motifs, producing a rather fussy 'pick'n'mix' result.