I went to the census of Ireland 1901 and 1911
1901/Antrim/Kirkinriola/Drumfane
house 6
David Montgomery, age 60
Rose, age 60
Catherine, age 30, daughter
Rose Mary, age 27, daughter
Lizzie, age 20, daughter
all born County Antrim, daughters all mill workers
1911/Antrim/Kirkinriola/Drumfare
house 18
Elizabeth Montgomery, age 30, Head of Family, single
Elizabeth Montgomery, age 9, daughter, scholar
Anne Jane Rooner, age 73, aunt, widow
This appears to be your Lizzie that immigrated with her daughter Lizzie in 1911. It would appear that she never married. She may have used Mrs. just to avoid the embarrassment and such that would accompany an unmarried woman with a child at that point in time.
This may be your John Montgomery in 1901 and 1911
1901/Antrim/Kirkinriola/Killylough
House 10
Margaret McCaughey, 49, head of family
John Montgomery, nephew, married, horsetrainer
Lizzie Montgomery, niece, married
It appears that John and Lizzie are married to each other and in the 1911 census he is listed as nephew in law. No children are listed for the couple.
Still trying to find info on the Elizabeth Montgomery who died in 1960 to see if she is your Lizzie.