I'm sorry that your question wasn't answered in a timely manner. We don't have many avian vets on this site.
Unfortunately, lethargy and diarrhea 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. With this in mind, your best course of action is to reach out to your county-extension poultry personnel or avian-oriented veterinarian (please see here: www.aav.org) for help.
It's best to approach the diagnostic process with a clear sense of her 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 worrisome symptoms you could tell me about - conjunctivitis, nasal discharge, sneezing, coughing, increased respiratory rate, gaping, regurgitation, vomiting, lameness, pale comb/wattles, repeated squatting as if to lay?
If you don't have an avian vet available to you, presumptive treatment for the most common gastrointestinal parasites plus a broad spectrum antibiotic are reasonable. Piperazine (Wazine, e.g.) will address roundworms and amprolium (Corid) will address coccidia. Tylosin (Tylan-50) dosed at 20-30 mg/lb once daily intramuscularly (or the injectable solution can be given directly into Carmella's beak) for 5-7 days is available in your local feed store as are the other drugs. It's best to bring her inside as shown here: http://www.the-chicken-chick.com/2015/02/how-to-help-sick-chicken.html
Please respond with further questions or concerns if you wish.