Cannot convert lambda expression to type "..." because it is not a delegate type

To add to Yuval's useful answer, if you just want to await an inline function, then the magic syntax is:

await ((Func<Task>)(async () =>
{
    //async function code
}
))();

Note the extra brackets on the end to call the lambda immediately after declaration. Obviously if your function returns a type, then it would be Func<Task<Whatever>>

Useful if you're using Task.WhenAny() for example to await both an inline function and a timeout task.

If you want an Anonymous Method, you'll have to declare one which returns a Task<Session> as it is marked with the async modifier, hence must return a void (only for async event handlers), Task or Task<T> :

Func<Task<Session>> anonFunction = async () => await fileService.ReadJsonAsync();

If all you do is run ReadJsonAsync, you may also save yourself the state machine generation like so:

Func<Task<Session>> anonFunction = fileService.ReadJsonAsync;

Then you can await on it higher up the call stack:

Func<Task<Session>> anonFunction = fileService.ReadJsonAsync;
await anonFunction();