Ronald Koeman opted to rest some of his first-team options on Thursday (19 October) with Idrissa Gueye left on the bench and Wayne Rooney and Phil Jagielka omitted from the match day squad completely.
Schneiderlin started however alongside Tom Davies in midfield, making a goal-saving challenge in the second-half to thwart Myziane Maolida and deny Lyon a second.
The former Manchester United midfielder appeared to pick up an ankle knock in making that challenge however and despite attempting to carry on, he was forced off after 57 minutes with Gylfi Sigurdsson coming onto replace him.
With the visit of Arsene Wenger's side just three days away, the France international is now likely to be a doubt for that clash.
Everton are already without a number of long-term absentees with Ross Barkley, Ramiro Funes Mori, Yannick Bolasie and Seamus Coleman still on the injured list. James McCarthy has also recently been sidelined with a knee problem but did return to play for the club's Under-23 side on Tuesday and could be an option to replace Schneiderlin on Sunday.
A defeat to Lyon extends Everton's run of games without a win to four, having won just two of their last 12 games with pressure mounting on Koeman every day. The Toffees found themselves a goal behind after just five minutes after Nabil Fekir coolly converted a penalty after full-back Fernando Marçal was clumsily taken out by Mason Holgate.
Ashley Williams looked to have earned his side a point with a thumping header that came just moments after the defender sparked a mass brawl between both sides, but nine minutes later, former Chelsea youngster Bertrand Traore found the back of the net with a backheeled effort which was aided by a deflection off Michael Keane.