Hi rdevine,
According to your description, I created three custom entities in CDS, Hospital, Reader, and Tray.
There is a picklist column “HospitalLocation” in the entity Hospital. Tray looks up to Reader, Reader looks up to Hospital.
Then create connections from PowerApps to the three entities.
On the app, add a Dropdown control, set its Items property as: Tray.TrayName.
Then add a label, set its Text property as
LookUp(Hospital,PrimaryId=LookUp(Reader,PrimaryId=LookUp(Tray,TrayName=Dropdown1.Selected.TrayName,Reader_.PrimaryId),Hospital_.PrimaryId),HospitalLocation)
This function will return the location within the hospital according to the TrayName selected in the dropdown control.
Hope this could be your reference.
Best regards,
Mabel Mao