Moodle.org sites are served via https. It would be logical to update all links to moodle.org sites to https equivalent.

So, have to performe everywhere in moodle code some search/replace, like :

• http://moodle.org to https://moodle.org
• http://docs.moodle.org to https://docs.moodle.org
• ...

Perhaps just don't modify file mod/lti/tests/locallib_test.php where on line 177 you find:
$this->assertEquals('https://moodle.org', lti_ensure_url_is_https('http://moodle.org'));

Update script should update the docroot value in mdl_config table, when it's still the default one (http://docs.moodle.org).

Changes should also be done in language packs (but perhaps in another tracker item).

Dev documentation should also reflect this change.

You can also look at the related discussion.