Substitute Sara Dabritz scored in extra-time at Stamford Bridge to give Lyon a 2-1 aggregate lead and seemingly send the hosts out after Vanessa Gilles had netted late in the second half to force the extra period.
Then, with two minutes of injury time played at the end of extra-time, Chelsea striker Lauren James advanced inside the box and was tripped. After a protracted VAR check, Maren Mjelde stepped up and buried her spot-kick to send the tie to penalties.
From there, Chelsea's luck held as they won the shootout 4-3, with Kerr among the successful penalty takers.
Lyon's US international Lindsey Horan saw her kick saved by Chelsea goalkeeper Ann-Katrin Berger to put Emma Hayes' side into the last four and keep intact their dream of an unprecedented treble.
The Blues next take on Barcelona, who had advanced 6-1 on aggregate against Roma.
Earlier on Thursday night, two-time champions Wolfsburg beat Paris St Germain 2-1 on aggregate and they next meet in-form Australian international Caitlin Foord and her Arsenal teammates in the other semi-final.
Chelsea had had the better of the first half against their French opponents after weathering early pressure.
Kerr and James were a threat every time they took possession in the Lyon half, and there was a palpable confidence to the Blues as they looked to move a step closer to a first European crown.
Yet with a single-goal aggregate lead, they remained vulnerable against a side that has won this tournament on six of their last seven attempts.
Chelsea's luck ran out 13 minutes from the end of normal time when Horan's cross was pulled back as far as Gilles, who beat the flat-footed Magdalena Eriksson to the ball and turned it inside Berger's post.
The quarter-final looked destined to be won on penalties was until Dabritz's decisive intervention at the end, taking a touch as Eriksson failed to cut out a cross and guiding the ball back across goal into Berger's far corner.
Then, after 127 minutes of play, came James' tumble, Mjelde's leveller and Berger's heroics to put the hosts through.
A 1-1 draw at the VW Arena was enough for German side Wolfsburg to progress to the semis.
They had been in the driving seat after winning 1-0 at the Parc des Princes last week and went further ahead through Alexandra Popp's goal in the 20th minute.
Popp's superb strike into the far corner prompted PSG to push hard for an equaliser and they deservedly got it when Kadidiatou Diani headed home a cross past goalkeeper Merle Frohms just 10 minutes later.
