Along with Tom Markel and Randi Bryce, she was a member of the second landing party to head to the surface of Lactra VII following the disappearance of the first group. Randolph and her party were then captured by the Lactrans. While in captivity, she developed a high fever that neither Markel nor Bryce could abate.
When a landing party from the USS Enterprise joined the Ariel landing party in captivity, Bryce informed them of Randolph's condition and that she was in the house. Though initially unable to access his medkit, Doctor Leonard McCoy diagnosed her with a malaria-type disease, caused by an insect bite. He was ultimately able to treat her after the Lactrans sensed the captives' thoughts, realized the situation, and returned his medkit to him. (TAS: "The Eye of the Beholder")