Having won the first leg 1-0 in France prior to the coronavirus shutdown in March, Memphis Depay scored a 13th minute penalty to provide the Ligue 1 side the vital away goal at Juventus Stadium.
Ronaldo gave Juventus hope when the Portugal star converted from the spot himself minutes before halftime following a controversial handball call on Depay.
Ronaldo scored again in the 60th minute on a booming shot from outside the box that clipped the hands of outstretched Lyon keeper Anthony Lopes and into the net.
The brace means that Ronaldo finishes the season with most goals in a single campaign for Juventus with 37. He beat the 35-goal tally of Ferenc Hizrez -- a goalscoring record which stood for 95 years.
But the record will mean little as neither Ronaldo nor his side could get the crucial third goal of the evening needed to win, the first time since 2015-16 that Juve fail to get to the quarterfinals.
"I actually expected less from us, I think we played a great game. We fell behind to a penalty kick that could have made us lose our heads and we had three chances when we were 2-1 ahead," Juventus coach Maurizio Sarri said after the match.
"We knew we needed courage, talent and a little bit of fortune," said Lyon coach Rudi Garcia. "We played a very good first leg as well but, with Cristiano Ronaldo, we knew we could have been knocked out at any moment.
The last time Ronaldo failed to reach that stage of in the competition was in his first season with Real Madrid (2009-10).
Depay's goal didn't come without some controversy as Rodrigo Bentancur appeared to get the ball cleanly off Houssem Aouar but referee Felix Zwayer pointed to the spot and chose not to look at the incident on the pitchside monitor.
The Dutch star then converted with a cheeky Panenka-style penalty which sent Wojciech Szczesny the wrong way.
The defeat left Juventus Sarri in an uncomfortable position as the Champions League title eluded the Turin side for another season.
Although Juventus have won Serie A for nine seasons in a row, they have not been able to get their hands on the European trophy since 1996 when they won it for the second time.
Despite continuing the domestic run, Sarri failed to give Juventus the flamboyant touch the club had been looking for as well as missing out on their main goal.
When asked whether he feared he would lose his job, Sarri said he found that question "offensive."
"I don't think top-level executives decide based on a single game," he said. "I think they make wider evaluations -- whether they be for or against."
"We don't need to put limits for us," Garcia added. "We are one of the best eight teams in Europe, we know Manchester City are a better team but it's just one game, so our goal is the semifinal."
The subsequent rounds will be one-legged affairs at neutral sites in Lisbon, culminating with the final on Aug. 23.
Information from Reuters was used in this report.