At least as of right now, I'm sure the Lightning have a pinpoint heartbreak moment in their history. They have some real bad losses, especially in recent years, but heartbreak will often times come in the form of losing winner-take-all games in OT, or something to that effect. Things that might be heartbreak moments in retrospect - think the Drouin goal in Game 6 against PIT in 2016 that was waived off for offside - weren't known to be heartbreaking moments at the time, and only might have become so in retrospect.
I can't find an iso video of it on YouTube, but the best answer is probably Andrew Shaw's eventual GWG in Game 5 of the '15 SCF. I think the Lightning had just missed a chance on the other end, the 'Hawks got a quick transition, and Shaw scored to give them the lead in the 3rd period. And they never trailed again the rest of the series. So, probably that.
But the Caps were FAR from perfect that year. In 2017 they WERE perfect. That's why I cited Game 7 2017 against Pittsburgh as the worst.
I feel that's a little bit of revised history. I remember thinking the Caps were going to murder the East that year. They had depth in attack and they had a young phenom, emerging goaltender in Varlamov (and Theodore was pretty decent that year IIRC). And if you remember, the ECF was eventually #7 vs. #8, so it's not like the rest of their fellow top contenders proved to be anything special either. Something was off with the Pens, and the other top seeds were the Devils and Sabres; neither of them figured to mount much of a threat.
And it's not like they lost because their D and goaltending hurt them. They lost because Halak stopped nearly 98% of the shots he faced in the last three games. Dude was in a flat-out zone. At least until the Caps finally won it all last year, if I were a Washington fan then I would still be having nightmares about what happened there. The only series I can think of that might've been a bigger shocker was perhaps in 2003 when the (Mighty) Ducks swept the Red Wings. I never expected the Habs to do what they did.