"Oh, don't I know the half of it! Last time I was here, a sentient pseudo-organic elevator was flying around trying to eat us instead! It was horrible! I'm called Faust, by the way - you'll forgive me if I'm unable to perform proper introductions at the moment!"

Outside of the brief pauses for air between each sentence, the good doctor seems relatively unfazed by the entire situation, almost as if he's merely enjoying a spot of afternoon jogging with his new acquaintance.
And to be fair, that is essentially what is currently happening - minus the rapid stomping of the monstrous feline blob in hot pursuit of fresh prey. If this thing is faster than the two of them...problems might begin arising.

"I don't wish to alarm you ma'am, but I'm as clueless as you are about this creature! I do not think we can run forever, but I am also incredibly unconvinced of our odds if we try to fight it! Any good ideas on your end?"

He's pretty sure dying here doesn't mean death in the waking world - but not sure enough to inform his ally of this theory, lest they then think to welcome the sweet embrace of furry oblivion in an ill-fated attempt to return home...