The Owls are unbeaten no more after a last-second 2-1 loss to the Scots in their American Midwest Conference opener on Saturday.
William Woods (5-1-1, 0-1) broke a scoreless tie on senior midfielder Luca Stroeter's unassisted goal in the 70th minute.
Lyon (3-2-1, 1-0) evened the match on junior midfielder Jonathan Ray's tally in the 77th minute on an assist from sophomore forward Abdullah Adam.
Scots senior midfielder Jack Hayes posted the game-winner with just two seconds left in regulation
Lyon edged the Owls out in shots 6-5. William Woods freshman goalkeeper Conor Cable finished with four saves.
The Owls host Park University in AMC play at 7 p.m. Wednesday.