For what it's worth, it does also work with lexical variables, but you need to declare them up-front...

use v5.10;
use strict;
use warnings;

sub delayed (&) {
    package delayed;
    use overload q[""] => sub { $_[0]->() }, fallback => 1;
    bless shift;
}

my ($person, $thing);
my $string = delayed {"Look $person, no $thing!"};

$person = "Ma";
$thing  = "stringy eval";

say $string;
[download]

Here's a version that eliminates the need to declare variables up-front, but does the interpolation manually using s///eg. It's pretty dodgy, and I wouldn't put it anywhere near production code, but it's quite cute as an example...

use v5.10;
use strict;
use warnings;

use PerlX::QuoteOperator delayed => {
    -emulate => 'q',
    -with    => sub ($) {
        package delayed;
        my $str = shift;
        use PadWalker;
        use overload q[""] => sub { $_[0]->() }, fallback => 1;
        my $get = sub {
            my $var = shift;
            my $my = PadWalker::peek_my(3);
            return $my->{$var} if exists $my->{$var};
            my $our = PadWalker::peek_our(3);
            return $our->{$var} if exists $our->{$var};
            die "No such variable: $var\n";
        };
        bless sub {
            my $_ = $str;
            s/(\$\w+)/${$get->($1)}/eg;
            s/(\@\w+)/join $", @{$get->($1)}/eg;
            return $_;
        };
    },
};

my $string = delayed "Look $person, no @thing!";
my $person = "Ma";
my @thing  = qw( stringy eval );

say $string;
[download]

It's cute, but the code that does the interpolation is pretty dodgy.