Problem:
Translated 404 page does not show up on requests to non-existent URLs in secondary language.
Solution:
Translate custom URL setting for the 404 to 301 - Redirect plugin.
Relevant Documentation:
In the WordPress dashboard, go to WPML → String Translation
In the "Select strings within domain:" drop-down, find admin_texts_i4t3_gnrl_options (or the relevant domain for the plugin being used for redirection), click Search
There should be a result similar to [i4t3_gnrl_options]redirect_link - or the relevant result containing the URL in the original language
Click on its Translations and insert the URL of the 404 page in secondary language
To get the URL, in WordPress admin dashboard go to Pages, click on the secondary language name above the pages list to show only pages in that language, find the 404 page, mouse over it and click "View", then copy the URL from the browser bar
