I do use the following combination :

• Thunderbird (Linux or Windows)
• Android (without any Gmail/google account)
• Zimbra mail server

And to get my address book synchronised, I installed the following softwares:

Thunderbird: Zindus

Android: CardDAV-Sync and Contact Editor Pro (make sure to install the last one to be able to edit contacts)

And use Zimbra and in Address Book tab, right click on Contacts and select Share address book:

And copy the URL bellow:

Then use this URL to set your configuration in Zindus:

and add a CardDAV account with the URL and you mail/password

and voilà, you have the 3 places synchronised on the go!