It was that he was in his third year of medical school at McGill University ... and determined to keep going from where he was, which on the day the NFL draft began meant he was amid a rotation in a neo-natal intensive-care unit.
So while family and friends and media were waiting for him in his Montreal apartment that day, he was detained for an emergency C-section with premature twins.
"There's protocol, you have to look for any meconium aspiration, you have to suction ... so you end up doing a lot," he explained upon his arrival in Kansas City as the Chiefs' sixth-round pick.
Words surely never before uttered by an NFL draft pick.
Immersed as he was, his intention to simultaneously continue pursuing his doctorate in medicine and the enormous physical and mental challenges of NFL line play _ especially with his raw roots in the game _ seemed daunting, if not downright preposterous.
Early on in all this, he said, "Right now, I have the feeling that I'm studying more (football) than I've ever studied for medicine."
So his graduation earlier this week, coupled with his development as an offensive-line fixture for the Chiefs, was momentous and cause for celebration from Canada to Kansas City.
"Congratulations Laurent! An incredible achievement that makes us proud," Justin Trudeau, the prime minister of Canada, wrote on Twitter.
This man is a treasure doing unprecedented stuff, and here's hoping the NFL is smart enough to relent on policy and allow the first of its active players to earn an M.D. to have that adorned to his name on his jersey.
"We're working on it," he said.
Whatever is to come of that, LDT radiated a certain joy about the achievement as he spoke Thursday after a Chiefs' offseason workout.
"It's been a great journey for the last four years," he said, smiling, while conceding he was glad it was over.
In this time of celebration, maybe it's easy to overlook how grueling and complicated it was to make this happen.
It started with LDT just being a unique and iron-willed person who made a promise to himself "to keep grinding and keep pushing to combine my two passions to the highest level and show people it was possible."
Not that he didn't wonder at times if he could or should keep trying to do both at once.
But he always came up with the same answer: "I love medicine, I love football, so why not (be) doing both?"
In moments of doubt, he summoned a vision of walking on the stage for graduation, relying on that when he had to rally to train in the offseason at 9 p.m. because he'd, say, just finished an emergency-department shift.
It could be just as draining during the season, as mentioned in a tweet sent by teammate Mitch Morse.
"I will never forget @LaurentDTardif studying the whole 11-hour plane ride back from London in 2015 after we had just played a game. It was just one example of the kind of work ethic and determination that Larry brings to everything he does. Congrats buddy, extremely proud of you."
The rest of that story: Duvernay-Tardif normally reserved any medical-school work for the offseason but had taken on an orthopedic-surgery exam during the bye week to follow that game.
So while the rest of the team was enjoying a victorious flight home, he lasered in for an exam he said he aced.
Another essential factor that Dorsey, coach Andy Reid and the Chiefs deserve credit for is being open to this fanciful idea (as was McGill, which worked with LDT on ways to make it happen).
Many coaches and organizations expressed skepticism in pre-draft visits.
"Medicine was kind of a question mark (for them): 'How do we know you really want to play football if you (are staying with) medicine?' " he recalled hearing around the league. "With Coach Reid, it was totally the opposite. ... I don't think it would have been possible if not for him."
As it happens, Reid's mother, Elizabeth, was a doctor of radiology who had studied at ... McGill.
"A great place," Reid called it Thursday, without letting on it had been the school of his mother _ whom the Reid family believes was among the pioneering females in the field.
So LDT remembers Reid telling him, "If you're here and you still have medicine as a Plan B, it's because you really love to play football, and I'm going to help you to the best of my ability. And that's what he's been doing for the last four years."
At their exit meetings every offseason, Reid would ask, "What's next for you, Doc?"
As for what's next now, LDT is giving himself a year before he moves toward the five years it will take to become an emergency physician.
That ambition relates to football, too, at least in terms of handling what he called the adrenalin rush.
"I think there are a lot of similarities between football and emergency medicine, you know?" he said. "You never really know in the emergency (room) what's going to step through the door. You've got to be able to, like, make rational decisions in really stressful environments and kind of take your emotion out of it.
"And there's a lot of similarity between that and trying to block a different pressure on third down (when) you've got to do it to convert."
Says the interesting fella who's made an epic conversion that both opens up the notion for others and stands as a marvel.
"You've got to love both if you want to succeed," he said, "because it was kind of hard."
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