>Morgan and his associates examined the books of the Knickerbocker Trust and decided it was insolvent, so they did not intervene to stop the run. Its failure, however, triggered runs on even healthy trusts, prompting Morgan to take charge of the rescue operation.[0]
[0] https://en.wikipedia.org/wiki/Panic_of_1907#J._P._Morgan
> As discussion ensued, the bankers realized that Morgan had locked them in the library and pocketed the key to force a solution, the sort of strong-arm tactic he had been known to use in the past. Morgan then entered the talks and advised the trust companies that they must provide a loan of $25 million to save the weaker institutions. The trust presidents were still reluctant to act, but Morgan informed them that if they did not it would lead to a complete collapse of the banking system. Through his considerable influence, at about 4:45 a.m. he persuaded the unofficial leader of the trust companies to sign the agreement, and the remainder of the bankers followed. Having received these commitments, Morgan allowed the bankers to go home.
You can tour the exact room where it all happened at the Morgan Library Museum in New York.
While that story is often repeated it sounds for sure apocryphal. A bunch of men from that day and age couldn't have figured out how to get out of that room? Or simply revolted and freaked out? Now maybe he feigned doing that or maybe he actually did 'lock the door' but so what? The story and legend value is just to much to ignore. It's almost certainly greatly exaggerated or not even close to being true. People can't even agree on news that happened in this day and age let alone the golden era of back in the day newspaper exaggeration.
In any case the 'lock' might have been some other leverage he used over the players that wouldn't make sense to the general public or make a good news story.
You're not thinking of this the right way. If a man had some health issue and needed to go to a hospital, or even if the men demanded to leave immediately, Morgan would have let them out. His locking the door was symbolic of his sense of urgency and determination to not leave the room without solving the crisis, something the others could tangibly see.