Why is my rabbit sick, not eating, has diarrhea, and is lethargic?

Hello there! I'm so sorry to hear that Flop is sick. Her condition sounds very serious, and I strongly suggest that you get her to a veterinarian immediately. Loose stool is abnormal for a rabbit, and can cause dehydration if it continues for more than a couple days - especially if she hasn't been drinking. Dehydration may be what is causing her to be lethargic, but her symptoms are relatively vague so I can't tell you from the information provided what is wrong with her. Parasites, bacterial or viral infection, foreign object ingestion, nutritional issues, and hairball impaction could all be possible causes, and without a veterinarian's help, a diagnosis will be difficult. At the vet's office, Flop will receive a full physical exam, and they will likely recommend x-rays and/or bloodwork to determine the cause of her illness. She will likely need fluid replacement therapy at the very least.

Something you can do to detect dehydration at home is a turgor test. When an animal has good skin turgor, it is hydrated - skin that snaps back into place when picked up has good turgor. Pick up a small amount of skin behind Flop's shoulders, and drop it - if it stays standing up or is slow to return to normal, she is likely dehydrated and needs immediate help. Do not force her to drink liquids as she may aspirate it into her lungs. Good luck, and I hope that Flop gets well!