After fiddling around for half an hour, here is how I got to configure Thunderbird as client for Gmail App Account.
1. Enable IMAP in Gmail App Mail Settings.
2. In Thunderbird, select Tools -> Account Settings.
3. Select Add New Account.
4. In the New Account Setup dialog, Select Email Account. Click on Next.
5. Set Your Name and Email Address in the Next Step. Click on Next.
6. In the Server Information, Select the type of incoming server as IMAP.
7. Enter the incoming server name as imap.googlemail.com (for outside US and imap.gmail.com for US).
8. Enter the outgoing server name as smtp.googlemail.com (for outside US and smtp.gmail.com for US). Click on Next.
9. Enter the Incoming User name as your email address (user@domain). I used firstname.lastname@example.org.
10. Enter the Outgoing User name as your email address. (e.g. email@example.com).
11. In the Account Settings Window displayed (Tools -> Account Settings), for the Server Settings, verify that the port number is 993.
12. In the Outgoing Server, set Port Number as 587, and for Use Secure connection, set TLS.
13. Now click on the Inbox. You will be asked for the password. And that completes it.