Lyon had gone in front after 17 minutes thanks to Kadidiatou Diani but Arsenal equalised through Mariona Caldentey's penalty.
Lyon coach Joe Montemurro, who managed Arsenal for four years and led them to a Women's Super League title, made a winning return though as his team were hit with wave after wave of attacks in the second half before Dumornay's finish.
Arsenal wasted several chances while Lyon were steadfast in defence, giving Renee Slegers' side a lot of work to do in the return leg on April 27 if they are to prevent the French club from reaching their 12th final in the competition.
Lyon took the lead when Diani was set through on the right wing and the French forward drilled her shot across Manuela Zinsberger in Arsenal's goal to find the far bottom corner.
The assistant's flag went up for offside to draw a roar from the home crowd but that quickly turned to groans when VAR confirmed Diani was onside by mere inches.
Arsenal's best chance came at the half-hour mark when an unmarked Frida Maanum saw her header at the far post go wide.
Lyon nearly doubled their lead minutes later when Dumornay spotted Zinsberger off her line and chipped the ball from nearly 40 metres, only for her effort to come off the crossbar.
The home side had one more chance to level on the stroke of halftime when Leah Williamson's header hit the bar, while the referee waved away penalty appeals when Katie McCabe appeared to be tripped in the box.
Arsenal played on the front foot in the second half and had two early chances to score, with Alessia Russo having a shot cleared off the line before Beth Mead's header flew wide.
Their pressure finally paid off from a corner when Lyon goalkeeper Christiane Endler failed to punch the ball clear and made contact with Williamson's head instead, with the referee awarding a penalty after a VAR check.
Caldentey stepped up and sent Endler the wrong way to bury her spot kick in the bottom corner after 78 minutes as the home crowd roared its approval.
However, any hopes of a comeback were snuffed out by Lyon four minutes later when Haitian striker Dumornay used her pace to power past the defence before pulling the trigger to make it 2-1, silencing the 40,000 fans at The Emirates Stadium.