Unless you are using OWIN in your API, you should have your Autofac configuration setup in your WebAPI like this, which is the standard way to configure Autofac for WebApi.
Include nuget pacakge Autofac.Integration.WebApi
var builder = new ContainerBuilder();
builder.RegisterApiControllers(Assembly.GetExecutingAssembly());
builder.RegisterType<MyType>();
var container = builder.Build();
var resolver = new AutofacWebApiDependencyResolver(container);
GlobalConfiguration.Configuration.DependencyResolver = resolver;
Should you need to request the LifetimeScope like in your example, you can then request this from GlobalConfiguration.
var scope = GlobalConfiguration.Configuration.DependencyResolver.GetRequestLifetimeScope();
MyService service = scope.Resolve<MyService>();