The Blues have reached the last four of the competition two years in a row and will be buoyed by the fact that Cuthbert was able to halve the aggregate deficit against a Lyon team that has won the Champions League in each of the last three seasons, and five times since 2011.
Chelsea went a goal down when Magda Eriksson scored an unfortunate second own goal in as many games. Lyon's lead was then doubled when Dzsenifer Maroszan whipped the ball in from a corner and Amandine Henry got the faintest of touches to flick it in.
What will give Chelsea hope ahead of the return home leg at Kingsmeadow next Sunday is that they had other chances to score. Fran Kirby had a penalty saved on the stroke of half-time, for example, while Maren Mjelde also tested Lyon goalkeeper Sarah Bouhaddi.
Cuthbert converted with just under 20 minutes remaining and it gave Chelsea a platform to end the game strongly against a Lyon side featuring Women's Ballon d'Or winner Ada Hegerberg.
It may be easier said than done, but a 1-0 win at home next weekend would send Chelsea through to the final in Budapest on 18 May.
The solitary away goal came courtesy of French midfielder Kheira Hamraoui and leaves Barça simply needing to avoid defeat back home in Catalonia next week to secure their passage to Budapest.
A testament to the growing strength of women's football at club in Europe, the Champions League duopoly enjoyed by French and German teams is now under serious threat this season.
Only one non-French or German club has reached the Women's Champions League final in the last 10 years. That was Swedish side Tyreso in 2014, with every other final 2010 a France versus Germany contest, or an all French affair in 2017 when Lyon beat Paris Saint-Germain.
The last time a team not from France or Germany won Europe's elite women's club competition was all the way back in 2007, when Arsenal lifted was then known as the UEFA Women's Cup.