Maureen, I'm sorry that your question wasn't answered in a timely manner. We don't have many avian vets on this site. How old is Lucy, please? How long has she been ill? What is the active ingredient(s) in the drench?
Unfortunately, her lethargy, anorexia, and paleness can indicate any number of illnesses or health issues in chickens. In avian medicine, there's rarely one cause of such a presentation, so we usually begin with a list of differential diagnoses and use lab tests, X-rays, and physical exams to differentiate one from another. Necropsy of a newly dead or a sacrificed severely ill bird then refrigerated (not frozen) can be an important diagnostic particularly in large flocks. I understand that you wouldn't want to sacrifice a pet, however.
It's best to approach the diagnostic process with a clear sense of Lucy's financial value to your operation. Although some services such as your county animal disease diagnostic laboratory might be available free of charge through a county agency or land-grant extension office, the expense of some diagnostic tests and treatments can add up quickly. While it’s always worth your time and money to identify a bacterial or viral infection that could potentially impact more than one member of the flock, this might not be the case with a condition that only affects one hen. It frustrates me that I can't be more specific for you but such is the dilemma of poultry owners and vets alike.
Are there any other symptoms that might help clarify why Lucy is behaving in that manner - a change in her eyes, sneezing, coughing, nasal discharge, increased respiratory rate, regurgitation/vomiting, swollen coelom (abdomen), paresis (weakness) or paralysis, squatting frequently as if to lay, or walking like a penguin?