Autofac and Func factories

I'm working on an application using Caliburn.Micro and Autofac.

In my composition root I'm now facing a problem with Autofac: I have to inject the globally used IEventAggregator into my FirstViewModel, and a second IEventAggregator that has to be used only by this FirstViewModel and it's children.

My idea was to make the second one be injected as Owned<IEA>, and it works, the container provides a different instance of IEA.

public FirstViewModel(
    IEventAggregator globalEA,
    IEventAggregator localEA,
    Func<IEventAggregator, SecondViewModel> secVMFactory) {}

The problem comes when I have to provide the event aggregators to the SecondViewModel.

To create the SecondViewModel I use a factory method as Func<IEA, SecondVM>. The SecondViewModel's constructor is the following:

public SecondViewModel(IEventAggregator globalEA, IEventAggregator localEA) {}

I want the container to inject the first as the registered one, and the second will be the IEA parameter of the Func<IEA, SecVM>.

this is the function I registered in the container:

builder.Register<Func<IEventAggregator, SecondViewModel>>(
     c =>
         (ea) =>
         {
             return new SecondViewModel(
                 c.Resolve<IEventAggregator>(),
                 ea);
         }
);

but when it gets called by the FirstViewModel I get the following error:

An exception of type 'System.ObjectDisposedException' occurred in Autofac.dll but was not handled in user code

Additional information: This resolve operation has already ended. When registering components using lambdas, the IComponentContext 'c' parameter to the lambda cannot be stored. Instead, either resolve IComponentContext again from 'c', or resolve a Func<> based factory to create subsequent components from.

I can't understand where the problem is, can you help me please, what am I missing?

Thank you.