Your instincts are correct. Their own studies show that the drug is not effective when delivered at late stages in the disease. https://www.nbcnews.com/health/health-news/lilly-antibody-drug-fails-study-hospitalized-covid-patients-other-trials-n1244900 To be effective, it must be taken earlier.
that is such a huge problem..no one wants to prescribe what might do some good while you are still at home.