The private IP (lan IP) is likely the Extended HELLO (EHLO) or HELLO (HELO).
You can change the HELO message:
Go to Thunderbird's
about:config page (in Preferences > Advanced > General > Config Editor).
mail.smtpserver.default.hello_argument preference (create it by right-clicking > New > String if it doesn't exist yet).
localhost as its value. Then that field in the Email header will contains
localhost instead of your private IP.
One example for your reference:
Received: from localhost (example.com [18.104.22.168])
(using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits))
(No client certificate requested)
(Authenticated sender: ...)
by ....com (Postfix) with ESMTPSA id 36C...;
Wed, 3 Jan 2018 18:22:39 -0800 (PST)