If you use tools such as GNU Privacy Guard to sign and or encrypt e-mail then you have the facility in Thunderbird, with the Enigmail extension to attach your public key (.asc file) to your e-mails. This is found as an option within the e-mail compose window.
Enigmail Menu — > attach My Public key.
However you can set up Thunderbird to either attach this by default or not attach by default. Which will give your a little more control.
Edit –> Account Settings –> OpenPGP security
Select the Advanced button near the bottom
From this dialogue you can select Attach my public key to messages.
Remember, to do this for each of your mail accounts.
One of the advantages with disabling: Some mailing discussion lists have a message size limit. Your message to the group could be well under 80k for example, BUT your public key can easily push the message size well over this. This will result in your message being rejected or stalled while it is approved.
If you want to include your GnuPG finger print (this is the long line of letters and numbers,) then you can attach this to a e-mail signature. Which is then included within the e-mail body at the bottom.
Edit menu –> Account settings and click the e-maul account (which is usually displayed as your e-mail address. From this section you can see there is a box for your signature.
Remember you may want to replicate the same signature text to each of your accounts OR replicate some of it, and delete or adjust to suit.
I am using version Thunderbird 60.4.0 – 64bit as a basis for this article. Previous or Future versions may differ slightly