Reacting to Boolean state in reactive ViewModels
You need to format your code neatly; this will improve readability, which will decrease bugs.  First, you have this:

public bool IsAuthenticated {
get { return _isAuthenticated; }
set { this.RaiseAndSetIfChanged (ref _isAuthenticated, value); }}


This should be:

public bool IsAuthenticated
{
    get { return _isAuthenticated; }
    set { this.RaiseAndSetIfChanged (ref _isAuthenticated, value); }
}


The if/else statement should be written like this:

IsAuthenticatedCommand.Subscribe (_ =&gt; {
    if (_) { this.IsAuthenticated = true; }
    else { this.NeedsToLogin = true; }
});


Also, you need to be consistent with your spacing; sometimes you have a space between braces, sometimes you don't:

if (_) { this.IsAuthenticated = true;} else {this.NeedsToLogin = true;}


I am no expert at lambda statements, but your lambda with the if/else looks fine to me.