Update: Did you ever want to just take back something ignorant? Yeah, all the time. So the original part of my post is left below for posterity to snigger at. And it's probably obvious that you can get your desired effect with a string-eval, with all the safety caveats that that implies. Nevertheless, here it is:

#!perl
use strict;
use warnings;

sub lambda {
  my $varname = shift;
  my $fn_body = shift;
  my $estring= "sub { my \$$varname = shift; $fn_body }";
  print "Evaling $estring\n";
  eval $estring;
}

my $x = 3;
my $closure = lambda 'x' => q { $x**2 };
for (1..4) {
  print $closure->($_), "\n";
}
print "And my X is $x\n";
[download]

--- original below ---

How close is this to satisfactory? (Packagery is just in there to test cross-package calling.) It's not actually using lexical x, but I can't see why that's important (though it could conceivably be, if your function were to call other functions).

#!perl
use strict;
use warnings;

sub lambda {
  my $varname = shift;
  my $fn = shift;
  my $pkg = do { no strict 'refs'; * {caller().'::'} };
  sub {
    local ${$pkg}{$varname} = \shift;
    $fn->()
  }
}

package a::b::c;

our $x;
my $closure = main::lambda 'x' => sub { $x**2 };
for (1..4) {
  print $closure->($_), "\n";
}
[download]