Lynch is leaving.
Mr. Jeruno looked at Lynch and truly didn't know how to keep Lynch here, let alone persuade him. He realized that he, or the President, wasn't what Lynch wanted, which left him clueless on what to use as bargaining chips!
You always need something others want in order to get what you want. Not a completely equivalent exchange, but at least both parties should find it suitable.
But now he was the one asking Lynch for something, yet there was nothing that Lynch must have or wanted, leaving him unable to speak.
It's not that he couldn't speak, but that he understood the meaning of speaking was minimal.
If he "forcefully" wanted Lynch to stay, it wasn't impossible, but at that point, Lynch would make exorbitant demands.
He would ask for all sorts of things that Mr. Jeruno couldn't afford or couldn't part with. Instead of preserving awkwardness, it's better not to do so now.
