Ah, think I might have found Lois in 1920, misspelt:
https://familysearch.org/pal:/MM9.1.1/MHNR-B6TOn Thomas' side, I think I can find a number of Thomas' relatives on familysearch, parents Francis and Mary (Mulcahy or variants), and this is probably them in 1880 with Thomas aged 18:
https://familysearch.org/pal:/MM9.1.1/MWS9-DL9 (Malachai's middle name was Patrick).
https://familysearch.org/pal:/MM9.1.1/M3FF-DQZ - this may be Thomas in 1900. Note that "home" is listed as Arlington, Washington, and he was married.
There is at
http://www.digitalarchives.wa.gov a birth in Arlington in 1895 for a boy (unnamed), legitimate son of Thomas McMahon, b. Lindsay, Ontario, 33, and Minnie Whitney (or Whiting?), b. Bay City, Michigan, aged 29. He was Minnie's fourth child.
Possibly in 1900:
https://familysearch.org/pal:/MM9.1.1/MMPR-9Y7Minnie was married "0" years to Mr Adam, four children, four living - the three Girow/Gerow kids and "T E McMahon".
Minnie Whiting m. John A Gerow in 1883 in Michigan (
https://familysearch.org/pal:/MM9.1.1/NQ3T-XYP )
John Albert Gerow remarried in Washington in 1898 (Washington Digital Archives)
William C Adams and Minnie Whiting married in 1900 in Washington (Washington digital archives).
"T E McMahon" may be this fellow in the 1920 census:
https://familysearch.org/pal:/MM9.1.1/MHN3-KFX(I think age of wife is wrong here, see below)
marriage:
https://familysearch.org/pal:/MM9.1.1/FLFB-B43possibly his wife with family in 1930 showing a grandson:
https://familysearch.org/pal:/MM9.1.1/XCQX-MP7Washington digital archives has her death in 1932 as Eva May McMahon
This would fit with Lois' testimony that her late husband had a son in Tacoma. It appears that this marriage did not last very long, so it's not surprising that Lois didn't know much of the detail.
It is possible that Minnie remarried at least once more and died as Minnie Belle Ryburn in Washington :
https://familysearch.org/pal:/MM9.1.1/N3B9-VQMWith husband in census in 1940 and 1930:
https://familysearch.org/pal:/MM9.1.1/K9S4-1MVI still can't find either of Thomas' marriages - to Minnie (possibly under either Whiting or Gerow or

) or to Lois. I wonder if either marriage took place in Alaska - records don't seem to be online.