The home side fell behind early on when Nabil Fekir slotted home a penalty following a rash challenge by Mason Holgate.
However, Ronald Koeman's side drew level after 69 minutes when Ashley Williams powered home a header, only for Bertrand Traore's deft backheel to hand Lyon the win six minutes later.
As a result, Everton have now taken just one point from their opening three Group E games and sit bottom of the table.
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