Is there an affordable transportation from LI to NYC for medical. elderly patient, no family

If the procedure is in hospital, most hospitals have social workers on staff that ought to know what services are available. The clinic or doctor's office that set up the procedure may know about options. Depending on health conditions, you might be able to hire someone through Uber or contact Area Agency on Aging in their city to see if they have any volunteers or know of low-cost options.