What would it take to cure someone of chronic Lyme disease?

Many issues. It takes longer to treat if you had the infection for a long time (a year or more) before starting treatment. Sometimes many months to 1-2 years. If you have multiple tick borne infections like babesia, bartonella, mycoplasma, various viruses, then treatment is extended to address these other infections, which need different drugs than what we use for lyme.
Question the Dx. I personally do not believe in the concept of chronic lyme disease. You may want to consult with an infectious disease specialist or a rheumatologist.