I don't know how much information you have on Lucy's parents and family so I will post what I found.
Federal Census of 1871 (Ontario Index)
District - York North, Sub District - King A
Edgar Harrison
b. England
occupation - tailor
Religion - Church of England
1881 Census of Canada
York North (137), King A, Div 2
Alice Harrison
age 47, b. Ireland, widow, catholic
Walter Harrison
age 17, b. Quebec, Church of Engl;and, farm labourer
Lucy Harrison
age 11, b. Ontario, occupation - servant
In the 1881 census, there is an Agnes Dick, b. Scotland, same district, sub dist and div.
This could match up with the information of Lucy in 1891 as a servant with a Dick family in Winnipeg.
1891 Census of Canada
District 131 North York, Township of King
20th April 1891
Harrison, Alice
age 50 (note the younger age) widow, b. Ireland, parents both born Ireland
Roman Catholic, no occupation listed
132 West York, St Albans Ward
Harrison, Walter
age 27, b. Ontario (instead of Quebec), father b. England, mother b. Ireland, methodist, occupation - teamster (horses)
wife Christina, age 24
Erla M or W age 2
Mildred M, age 8 months
There are Callaghan's (John and Mary and family members) in the same Ward as Walter Harrison. The Callaghan's are RC and Irish.
This doesn't prove that the Michael Callaghan (and alternate spellings) is your Michael but it does seem a good possiblity.
Paper trails were not as common at that point in time and people would change facts to suit the purpose at the time. It is possible that Lucy wasn't divorced from the first husband when she married the second. Do you have proof that she was divorced or are assuming that as she remarried. It was not uncommon at that point in time for a woman to leave her husband and state that he had died. Divorce would have been extremely uncommon and especially if they were catholic. If she was divorced, she would not be able to marry in a catholic church. On the 1900 Montana census that you have info for, does it have her and her husband as catholic. That could also explain the Michael found in the 1901 census would be listed as married.
Good luck with your search,
Val