I bet that this is a problema with Thunderbird version. Take a look at this bug reports on Ubuntu launchpad an Mozilla:
I'm trying to login in my gmail account.
After entering email and password I have a Google page with enter
But when I press the Continue button - nothing happens.
Screen in attachment.
Open Thunderbird and try to login in Gmail account with 2-auth.
1) Ubuntu 16.04.1 LTS x86_64
3) Continue authorization in Gmail
4) Pressing the continue button have no effect
- Thunderbird 45.8.0 hangs on new Gmail password window
Steps to reproduce:
Tried to create a new profile with a gmail account in ThB 45.8.0
GMail's Auth page appears, pre-filled with my email address, but
clicking on "Next" button has no effect, so the password cannnot be
verified, thus the account cannot be created. My problem is exactly
the one described here :
NOTE: my config already says that OAuth2 is selected...
GMail Auth window should work or an alternative way of
configuring/verifying the account should be proposed
Both bug reports refers exactly to Thunderbird version 45.8.0. Try a more recent version (like 54) and see if this still happens.