Several:

use Data::Dumper;
$Data::Dumper::Deparse = 1;

my $sub;
{
    my $x = "foo";
    $sub = sub {
        my $filename = shift;
        return "/tmp/$x/" . $filename;
    };
}

print Dumper($sub);
__END__
$VAR1 = sub {
            my $filename = shift @_;
            return "/tmp/$x/" . $filename;
        };
[download]

use Data::Dump::Streamer;

my $sub;
{
    my $x = "foo";
    $sub = sub {
        my $filename = shift;
        return "/tmp/$x/" . $filename;
    };
}

print Dump($sub);
__END__
my ($x);
$x = 'foo';
$CODE1 = sub {
           my $filename = shift @_;
           return "/tmp/$x/" . $filename;
         };
[download]

use B::Deparse;

my $deparse = B::Deparse->new;

my $sub;
{
    my $x = "foo";
    $sub = sub {
        my $filename = shift;
        return "/tmp/$x/" . $filename;
    };
}

print $deparse->coderef2text($sub),"\n";
__END__
{
    my $filename = shift @_;
    return "/tmp/$x/" . $filename;
}
[download]

update: added a block scope, from which you can see that out of those only Data::Dump::Streamer provides the sub's context.