[Her concern does actually get him to pause for a moment as they head toward the lifts. Jon looks over at her and while, he's desperately curious and needs to know what's down there... they don't have to risk the two of them. Probably, they shouldn't.]

You don't need to come down with me. Find the stairs and guard them. I'll come up to you again. It might be good to have a lookout.

[And safer for Ava... even if she is dead.]