Here I'm going to give you a simple snippet of "Retrieving the content type enabled lists" from the site using Client Object Model.

            ClientContext context = new ClientContext("http://localhost");
            Web web = context.Web;

   //Load all the lists from web
            ListCollection listCollection = web.Lists;   
   //Filters the lists has the content type enabled
            context.Load(listCollection,
                lists => lists
                    .Include(list => list.Title)
                    .Where(list => list.ContentTypesEnabled)                   
                );
   //Execute the Query
            context.ExecuteQuery();                    
            Console.WriteLine("Lists enabled with ContentType:");
   //Print the Content type enabled lists
            foreach (var list in listCollection)
            {
                Console.WriteLine(list.Title);
            }

The above code only returns the List collection from particular web, those are content type enabled.