To list mails and templates, I had to set lexik_mailer.simple_pager as public.
To edit a mail, I had to set lexik_mailer.form.handler.email as public.
To edit a layout, lexik_mailer.form.handler.layout has to be public.
I admit I don't know if I had to flag them as public in Resources/config/services.xml due to something special in my code (it was written a long time ago by someone else) or if it really is due to services being private by default in Symfony 4.