Lincoln only nods rather than bother trying to convince Jyn otherwise. He knows she's not in a good state right now and he doesn't want to make it worse for her in any way. She needs a friend right now, just to have someone nearby and Lincoln can do that.

He can be quiet, he can just be around, he can make Jyn as comfortable as he thinks she's going to be. It won't be everything, he can't fix this. But he can there for her.

So they leave without saying anything else. Lincoln figures there really isn't much else to say.