The '56 Lincoln is one of my all time favorites. In an era known for sometimes over the top styling, Ford kept the Lincoln elegant and understated while maintaining a futuristic theme. The transmission is nothing more than a heavy duty Ford-O-Matic, but few if any Fordo parts will interchange with the Turbo Drive. A short web search did not turn up any rebuild kits so it looks like you'll need to buy the needed parts individually. You might start here:
https://www.lincolnoldparts.com/ with a phone call. Another possibility is Kanter Auto Products:
https://www.kanter.com/index.aspx . eBay is another possibility, and these guys:
https://www.fatsco.net/. Also:
http://www.autotran.us/fmkits1.html . Good luck!