html sitemap via recursive function

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The “memory exhausted” error in question happened because of this part in your function: 'parent' => $next_page -> post_parent, which should actually be 'parent' => $next_page -> ID (or I’d omit the unnecessary spaces, i.e. I’d use 'parent' => $next_page->ID).

And the error can be illustrated like so:

$cur_page = get_post( 123 ); // assume the post_parent is 45
aiv_get_sibling_pages( $cur_page );
// 1. get_pages() is called with 'parent' set to 45.

// 2. Assume get_pages() returned page 123 as the 1st item.
// 3. Your `foreach` calls aiv_get_sibling_pages( <the post object for page 123> )

// 4. .. and then the loop restarts at step 1 and never ends..
// eventually, PHP exits with the "memory exhausted" error :(

So as I said earlier, use 'parent' => $next_page->ID and the memory error would be gone.

But I would also make these changes:

  1. Before the $out .= '<ol>';, add this:

    // Don't add the OL if there are no more pages.
if ( empty( $pages ) ) {
    return '';
}

  2. The get_pages() in the foreach is not necessary. So,

    // Replace this:
$child_pages = get_pages('child_of=" . $page->ID);
if(count($child_pages) > 0) {
    $out .= aiv_get_sibling_pages($next_page);
}

// with just:
$out .= aiv_get_sibling_pages( $next_page );

And actually, you could use wp_list_pages()..

Something like this:

$list = wp_list_pages( array(
    "child_of' => 123, // just change 123 to the correct ID
    'title_li' => '',
    'echo'     => false,
) );

echo '<ol>' . str_replace(
    [ '<ul>', '<ul ', '</ul>' ],
    [ '<ol>', '<ol ', '</ol>' ],
    $list
) . '</ol>';

But yes, if you want full control over the HTML, then your custom function would be easier in that case.