You can only use the language variables, if you have set at least one language in the config.php file.
If you don’t want to enable multi-language support, you can define strings in your config file, using c::set() and c::get() instead of l::set() and l::get().
I would add the needed strings as a field (type: text) for every string in the corresponding blueprint, may be of the parent page to avoid the same field on many pages.
Or add these fields on /site/blueprints/site.yml or a hidden admin-page.