package Foo;

use 5.012;
use strict;
use warnings;

$Foo::V = "fred";

{
    local our $V = "waldo";

    say $V;
    sub bar {say $V};
    sub set_v {$V = shift};
}

package Baz;

Foo::bar;
Foo::set_v "fnord";
Foo::bar;

__END__
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Running this gives output:

waldo
fred
fnord
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Removing the local, and running it gives:

waldo
waldo
fnord
[download]

And it won't compile if, instead of removing the local, you remove the our.

Of course, you may argue this code isn't very useful, but it does show there can be differences between local, our and local our. Given that I don't use our much (typically just for @ISA, and @EXPORT and friends), and neither local, I don't think I've ever had the need to use local our.