Lavellan looks away but, notably, he doesn't correct him.

Instead he turns silently on his heel and leads Rinzler on a winding path elsewhere in the facility. It's slow going, because of his injury and because he'd been here before in a different context and he doesn't quite remember where everything is. But eventually they come to a hallway lined with a multitude of uniformly featureless doors, and Lavellan stops and steps aside. Apparently, he's reluctant to actually go in any of them.

Rinzler can do what he wants from here; Lavellan did his part.