my $x = 1;
my $f = sub { $x };
{
    $x = 2;
    print $f->(), "\n"; # => 2
}
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It's not the dynamic-scoping-like behaviour that's the problem

Yes, it is:

The real difficulty (for me, anyway) is making a change in an inner scope to a lexical variable in an outer scope in such a way that the change will ‘revert’ outside that scope.

That's the dynamic scoping you're after.

Make $x a package variable, use local, and it will work the way you want. I don't see the point of making $x a lexical if you don't want lexical behaviour.

I'm sorry; I know that I must be mis-using the terms, but it seems to me that what I'm looking for is not contrary to what one could expect of lexicals. Making a change in an inner scope that is ‘seen’ by an outer scope is what I mean by “dynamic scoping” (although I probably shouldn't), and that is, of course, no problem. Having changes to a variable within a scope undone at the end of that scope is just what scoping means—it seems to me that it has nothing to do with lexical vs. dynamic. Again, aside from magic that can be associated to copying,

{
    my $temp = $x; $x = $new;
    ...
    $x = $temp;
}
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does what I want, obviously without subverting Perl in XS-y ways.

Is it really the case that setting aside a value to be restored at the end of scope is what is meant by “dynamic scoping”?