Seems you just want a complicated way of not writing $_[0] in the sub. That can be done of course. But why would you? And what has this to do with localizing a lexical, which you were asking about in your earlier posts? If you're passing in the parameter to the sub, there's no need to localize anything, is there?

1. Yes, that's right (for the lambda example).
2. Skipped.
3. Why not?
4. Only that localising a lexical was my first thought for how to implement it. (Example code is at Local for lexicals.) Once I thought of the problem in that context, it immediately seemed to crop up many other places.
5. You are certainly right that there are ways to do it without localisation. If I write out the sub—as you've done here:

   my $f = sub {my $x = shift; sub {$x ** 2}->()};
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   (formatted, I think, specifically to be faithful to my original attempt), or even more briefly as just:

   my $f = sub { my $x = shift; $x**2 }
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   then it certainly works. I would just like to avoid the slight extra verbiage and write instead

   my $f = lambda $x => sub { $x**2 }
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   as syntactic sugar (well, for some definition of ‘sugar’) for the same thing.