Were all children of Garrett & Jane born in Lancashire? Have you found their baptisms?
Baptisms at St. Mary of the Assumption, Burnley.
https://lan-opc.org.uk/Burnley/Burnley/stmary/index.htmlFather's name Geraldus, the Latin form of Gerald. Various transcriptions of mother's surname including Lanney and Ladney.
First child baptised at the church was Maurice Gerald 1861. Godfather Patrick Barry.
A Catherine Barrey was godmother for Jeremy Barry 1865.
Also, baptisms of children of Garrett's 2nd marriage to Ann Doyle. A Patrick Barry was godfather of Ann Barry 1876.
Some children of Patrick Barry & Mary (Guilfoyle/Guilfoy) baptised at St. Mary included:
Gerald 1869
John Robert 1871, godfather Gerald Barry
Marriages at St. Mary of the Assumption, Burnley:
1873 Gerald Barry & Ann Doyle; groom's father Gerald Barry; witness Patrick Barry
Note says Groom's first name Garrett on marriage registration.
1866 Patrick Barry & Mary Gilfoy; groom's parents Gerald & Helen Barry
1864 Patrick Barry & Ellen Redman; groom's father Gerald Barry
Another Garrett Barry married at St. Mary of the Assumption
1852 Garret Barry & Bridget Gibbons; groom's parents Richard & Nanny*
(There was another Gibbons wedding on the same day)
*Nanny/Nancy may be a variant of Ann.
That Garrett & Bridget Barry may have been living at Shed Street, Burnley on 1861 census. Surname transcribed Berry on Family Search. Garrett's birth info on census was Ireland 1834. A Garrett Barry of an appropriate age died 1868.
Other Barry couples who had children baptised at St. Mary of the Assumption and who may have been related to either Garrett Barry (or to both of them):
Maurice Barry & Jane/Joan/Joanna (GLENNY). Their daughter Lucinda (Lucy?) was baptised 1869. A note says that father's name had Garrett written above it.
John Barry & Ann (BURKE) had several children baptised there including Thomas 1873 (godparents Garrett Barry, Bridget Barry) and Gerald 1877. John & Ann married 1869. John's parents were Richard & Ann, so he was possibly a brother of the Garrett Barry who married Bridget Gibbons in 1852.