I was successfully using Thunderbird with iCloud mail on an iCloud equipped WinX computer until I foolishly changed the iCloud password. Now the iCloud server will not recognize the new password through Thunderbird. Does this make this statement on Apple Support pages a lie: "If you are signed in to iCloud for Windows, you don't need an app-specific password when using your Apple ID with third-party Microsoft apps."?
Thunderbird is not a Microsoft app, so you may indeed need to set up an app-specific password. In order to do this you need to set up two-factor authentication for your Apple ID, and for this you need to have either a Mac running el Capitan or above, or an iOS device running iOS9 or above.
Two-factor authentication for Apple ID - Apple Support
Using app-specific passwords - Apple Support
If you are unable to set up two-factor authentication you should set up 2-step verification and use that to create an app-specific password (see link below) . Then go to https://appleid.apple.com , select 'Password and Security'; click 'Generate an App-Specific Password' and follow the instructions. Once you have the password, copy it and paste it into the password field in the application instead of your usual iCloud password. You should also keep a note of it (though you can generate a new one if required).
Two-step verification for Apple ID - Apple Support
You will need to nominate a 'trusted device': any phone capable of receiving SMS messages. There will be a 2-day wait before you can complete the process.
(A particular caveat (about 2-step only) - you will be issued with a 'Recovery Key' in case you lose your 'trusted device'. Make sure to write this down and keep it in a safe place; if you lose both it and your trusted device you will be permanently locked out of your ID. You'd be surprised at the number of people who've posted here that they've got themselves into just that position.)
third party email client
