I recently lost my medical due to a lung transplant. I may be able to get a 3rd class but probably not a 2nd class. I have been asked to fly SIC for a 135 charter on demand, flying a turboprop, autopilot in lieu of a SIC that carries 8 passengers.( Note autopilot in lieu of SIC ) Some customers want a SIC even though it is not required. Can I do this with a 3rd class medical or even no medical?

If you can hold a third class you should try and get a SODA for the Second class!

https://www.faa.gov/about/office_org.../appeals/soda/

61.23 says you need a second class to exercise the privileges of a commercial certificate and a third for a private. 135.245 says you must hold a commercial to be SIC. So even if you're operating under the autopilot in lieu of, if you're going to be an SIC you have to hold a second class.