compliance with GDPR

at the moment this is not yet available by default, however, we asked the Devs about this for additional confirmation.

Hello, I don’t know how that GDPR plugin works, but our plugin has the action ‘register_form’ in the reigstration form template. We basically mimick the form you see on the regular WP registration page, so in theory any plugin that adds fields to it via that action should show up on ours too.

Does the plugin add a checkbox to the regular WP registration form?

If not, then adapting your code, this should work on both LWA and the standard WP registration form

add_action('register_form', function() {
  gdpr('consent')->register('my_custom_newsletter_consent', 'I want to receive a weekly newsletter from you');
});