The Blues needed to avoid defeat and hope that Atalanta were unable to do the same at Apollon Limassol in the night's other Group E fixture, but neither result went their way.
Lyon edged a tense first half and almost took the lead in the 23rd minute when Everton goalkeeper Jordan Pickford parried Bertrand Traore's header at full stretch, before denying Nabil Fekir on the follow-up.
There was a blow for the visitors in the 39th minute when defender Cuco Martina fell awkwardly from an aerial challenge, leaving the field on a stretcher in a neck brace before being ferried to hospital for an overnight stay.
Despite losing a man to injury and reshuffling their backline as a result, the Blues defended well in the opening stages, keeping the hosts' chances to a minimum and tried to take the game to their opponents in the second half.
Everton almost found themselves in front moments after the restart when the ball fell kindly for Idrissa Gueye just inside the box, the midfielder letting fly but failing to get enough power behind his shot to trouble Lyon keeper Anthony Lopes.
The English side were left reeling in the 68th minute when Morgan Schneiderlin slid in for a challenge, only to deflect the ball into the path of Traore in front of goal, allowing the former Chelsea forward to place a strike beyond Pickford and into the net.
From there, the Toffees capitulated, falling further behind in the 76th minute when substitute Houssem Aouar collected a reverse pass from Memphis Depay and curled a shot into the bottom corner to double the hosts' lead.
When Everton were reduced to 10 men in the 80th minute thanks to a rash challenge from the already-booked Schneiderlin, they only looked like conceding again ahead of the full-time whistle.
The inevitable occurred two minutes before the end as Depay latched on to Jordan Ferri's through-pass and placed Lyon's third beyond Pickford to cap off another miserable night for managerless Everton.
The defeat, coupled with Atalanta's 1-1 draw in Cyprus, was enough to end the Blues' Europa League campaign after four matches and put Lyon in good stead to reach the knockout phase.
A return of one point from three Europa group stage games was already the worst by a Premier League club, a run of form that leaves them bottom of Group E with only pride to play for in their remaining two fixtures.