The Doctor watches her go, then picks a little more at the food she'd prepared for him -- which is actually quite good -- before slipping back down to the medical bay to check on the status of his scan. Still running; will probably take hours to complete. No harm, then, in just leaving it to run while they nip off to the lake.

A few more minutes later, and he strolls on up to the console room to wait for Thirteen to finish getting ready.