It will be just the second time the Hammers have faced French opposition in European competition after beating Metz in the 1999 Intertoto Cup final.
Giovanni van Bronckhorst's side reached the last eight thanks to a 4-2 aggregate win against Red Star Belgrade of Serbia.
Should West Ham reach the semi-finals they could meet Barcelona if the Catalan giants overcome Eintracht Frankfurt, while Rangers will face either German club RB Leipzig or Atalanta of Italy if they reach the last four.
The draw means the earliest the two British sides can meet is in the final.
The two-leg quarter-finals will take place on 7 and 14 April, the semi-finals are on 28 April and 5 May with the final in Sevilla's Ramon Sanchez-Pizjuan Stadium on Wednesday, 18 May.
Europa League quarter-final draw
RB Leipzig v Atalanta
West Ham v Lyon
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