I have my settings in Thunderbird set to smtp.gmail.com port 587 STARTTLS Authn: Normal password

Change your settings for the OUtgoing Server/SMTP as per below: server name: smtp.gmail.com port: 465 connection security SSL/TLS authentication method: OAuth2

For the incoming server change 'authentication method' to 'OAuth2' as well.

I tried that and got the below when trying to send an email through Thunderbird: Sending of the message failed. The message could not be sent because the connection to Outgoing server (SMTP) smtp.gmail.com timed out. Try again.

I don't see any choice for Oauth2 for the incoming (POP) server settings for the gmail server.

Please post your Troubleshooting Information. At the top right of the Thunderbird window, click the menu button , then select Help > Troubleshooting Information. Press the Copy text to clipboard button and paste the information into your reply.

I don't see any choice for Oauth2 for the incoming (POP) server

You're quite right, OAuth2 is for IMAP only. Sorry about the confusion.

Application Basics

   Name: Thunderbird
   Version: 38.4.0
   User Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:38.0) Gecko/20100101 Thunderbird/38.4.0
   Profile Folder: Show Folder
             (Local drive)
   Application Build ID: 20151119061742
   Enabled Plugins: about:plugins
   Build Configuration: about:buildconfig
   Memory Use: about:memory

 Mail and News Accounts
   account1:
     INCOMING: account1, , (none) Local Folders, plain, passwordCleartext

   account3:
     INCOMING: account3, , (pop3) mail.lonex.com:143, SSL, passwordCleartext
     OUTGOING: smtp.gmail.com:465, SSL, OAuth2, true

   account4:
     INCOMING: account4, , (pop3) pop.gmail.com:995, SSL, passwordCleartext
     OUTGOING: smtp.gmail.com:465, SSL, OAuth2, true

 Crash Reports

 Extensions
   CompactHeader, 2.1.0, true, {58D4392A-842E-11DE-B51A-C7B855D89593}
   Lightning, 4.0.4.1, true, {e2fda1a4-762b-4020-b5ad-a41df1933103}
   Zindus, 0.8.42, true, {ad7d8a66-253b-11dc-977c-000c29a3126e}
   Provider for Google Calendar, 1.0.4, false, {a62ef8ec-5fdc-40c2-873c-223b8a6925cc}

 Important Modified Preferences

   Name: Value

     accessibility.typeaheadfind.flashBar: 0
     browser.cache.disk.capacity: 358400
     browser.cache.disk.smart_size_cached_value: 358400
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size.use_old_max: false
     extensions.lastAppVersion: 38.4.0
     font.internaluseonly.changed: false
     font.name.monospace.el: Consolas
     font.name.monospace.tr: Consolas
     font.name.monospace.x-baltic: Consolas
     font.name.monospace.x-central-euro: Consolas
     font.name.monospace.x-cyrillic: Consolas
     font.name.monospace.x-unicode: Consolas
     font.name.monospace.x-western: Consolas
     font.name.sans-serif.el: Calibri
     font.name.sans-serif.tr: Calibri
     font.name.sans-serif.x-baltic: Calibri
     font.name.sans-serif.x-central-euro: Calibri
     font.name.sans-serif.x-cyrillic: Calibri
     font.name.sans-serif.x-unicode: Calibri
     font.name.sans-serif.x-western: Calibri
     font.name.serif.el: Cambria
     font.name.serif.tr: Cambria
     font.name.serif.x-baltic: Cambria
     font.name.serif.x-central-euro: Cambria
     font.name.serif.x-cyrillic: Cambria
     font.name.serif.x-unicode: Cambria
     font.name.serif.x-western: Cambria
     font.size.fixed.el: 14
     font.size.fixed.tr: 14
     font.size.fixed.x-baltic: 14
     font.size.fixed.x-central-euro: 14
     font.size.fixed.x-cyrillic: 14
     font.size.fixed.x-unicode: 14
     font.size.fixed.x-western: 14
     font.size.variable.el: 17
     font.size.variable.tr: 17
     font.size.variable.x-baltic: 17
     font.size.variable.x-central-euro: 17
     font.size.variable.x-cyrillic: 17
     font.size.variable.x-unicode: 17
     font.size.variable.x-western: 17
     gfx.blacklist.suggested-driver-version: 257.21
     gfx.direct3d.last_used_feature_level_idx: 0
     mail.openMessageBehavior.version: 1
     mail.winsearch.firstRunDone: true
     mailnews.database.global.datastore.id: 8d3489c2-6aeb-485e-9518-8a615fe8f7d
     mailnews.database.global.views.conversation.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"3"},"attachmentCol":{"visible":false…
     network.cookie.lifetimePolicy: 2
     network.cookie.prefsMigrated: true
     network.predictor.cleaned-up: true
     places.database.lastMaintenance: 1449948743
     places.history.expiration.transient_current_max_pages: 104858
     places.history.expiration.transient_optimal_database_size: 167772160
     plugin.importedState: true
     print.print_printer: IBMLaser1412
     print.printer_Brother_HL-2280DW_Printer.print_bgcolor: false
     print.printer_Brother_HL-2280DW_Printer.print_bgimages: false
     print.printer_Brother_HL-2280DW_Printer.print_colorspace:
     print.printer_Brother_HL-2280DW_Printer.print_command:
     print.printer_Brother_HL-2280DW_Printer.print_downloadfonts: false
     print.printer_Brother_HL-2280DW_Printer.print_duplex: 0
     print.printer_Brother_HL-2280DW_Printer.print_edge_bottom: 0
     print.printer_Brother_HL-2280DW_Printer.print_edge_left: 0
     print.printer_Brother_HL-2280DW_Printer.print_edge_right: 0
     print.printer_Brother_HL-2280DW_Printer.print_edge_top: 0
     print.printer_Brother_HL-2280DW_Printer.print_evenpages: true
     print.printer_Brother_HL-2280DW_Printer.print_footercenter:
     print.printer_Brother_HL-2280DW_Printer.print_footerleft: &PT
     print.printer_Brother_HL-2280DW_Printer.print_footerright: &D
     print.printer_Brother_HL-2280DW_Printer.print_headercenter:
     print.printer_Brother_HL-2280DW_Printer.print_headerleft: &T
     print.printer_Brother_HL-2280DW_Printer.print_headerright: &U
     print.printer_Brother_HL-2280DW_Printer.print_in_color: true
     print.printer_Brother_HL-2280DW_Printer.print_margin_bottom: 0.5
     print.printer_Brother_HL-2280DW_Printer.print_margin_left: 0.5
     print.printer_Brother_HL-2280DW_Printer.print_margin_right: 0.5
     print.printer_Brother_HL-2280DW_Printer.print_margin_top: 0.5
     print.printer_Brother_HL-2280DW_Printer.print_oddpages: true
     print.printer_Brother_HL-2280DW_Printer.print_orientation: 0
     print.printer_Brother_HL-2280DW_Printer.print_page_delay: 50
     print.printer_Brother_HL-2280DW_Printer.print_paper_data: 1
     print.printer_Brother_HL-2280DW_Printer.print_paper_height: 11.00
     print.printer_Brother_HL-2280DW_Printer.print_paper_name:
     print.printer_Brother_HL-2280DW_Printer.print_paper_size_type: 0
     print.printer_Brother_HL-2280DW_Printer.print_paper_size_unit: 0
     print.printer_Brother_HL-2280DW_Printer.print_paper_width: 8.50
     print.printer_Brother_HL-2280DW_Printer.print_plex_name:
     print.printer_Brother_HL-2280DW_Printer.print_resolution: 0
     print.printer_Brother_HL-2280DW_Printer.print_resolution_name:
     print.printer_Brother_HL-2280DW_Printer.print_reversed: false
     print.printer_Brother_HL-2280DW_Printer.print_scaling: 1.00
     print.printer_Brother_HL-2280DW_Printer.print_shrink_to_fit: true
     print.printer_Brother_HL-2280DW_Printer.print_to_file: false
     print.printer_Brother_HL-2280DW_Printer.print_unwriteable_margin_bottom: 0
     print.printer_Brother_HL-2280DW_Printer.print_unwriteable_margin_left: 0
     print.printer_Brother_HL-2280DW_Printer.print_unwriteable_margin_right: 0
     print.printer_Brother_HL-2280DW_Printer.print_unwriteable_margin_top: 0
     print.printer_IBM_Infoprint_1412_Laser.print_bgcolor: false
     print.printer_IBM_Infoprint_1412_Laser.print_bgimages: false
     print.printer_IBM_Infoprint_1412_Laser.print_command:
     print.printer_IBM_Infoprint_1412_Laser.print_downloadfonts: true
     print.printer_IBM_Infoprint_1412_Laser.print_evenpages: true
     print.printer_IBM_Infoprint_1412_Laser.print_footercenter:
     print.printer_IBM_Infoprint_1412_Laser.print_footerleft: &PT
     print.printer_IBM_Infoprint_1412_Laser.print_footerright: &D
     print.printer_IBM_Infoprint_1412_Laser.print_headercenter:
     print.printer_IBM_Infoprint_1412_Laser.print_headerleft: &T
     print.printer_IBM_Infoprint_1412_Laser.print_headerright: &U
     print.printer_IBM_Infoprint_1412_Laser.print_in_color: true
     print.printer_IBM_Infoprint_1412_Laser.print_margin_bottom: 0.5
     print.printer_IBM_Infoprint_1412_Laser.print_margin_left: 0.5
     print.printer_IBM_Infoprint_1412_Laser.print_margin_right: 0.5
     print.printer_IBM_Infoprint_1412_Laser.print_margin_top: 0.5
     print.printer_IBM_Infoprint_1412_Laser.print_oddpages: true
     print.printer_IBM_Infoprint_1412_Laser.print_orientation: 0
     print.printer_IBM_Infoprint_1412_Laser.print_pagedelay: 500
     print.printer_IBM_Infoprint_1412_Laser.print_paper_data: 1
     print.printer_IBM_Infoprint_1412_Laser.print_paper_height: 11.00
     print.printer_IBM_Infoprint_1412_Laser.print_paper_size: 1713399662
     print.printer_IBM_Infoprint_1412_Laser.print_paper_size_type: 0
     print.printer_IBM_Infoprint_1412_Laser.print_paper_size_unit: 0
     print.printer_IBM_Infoprint_1412_Laser.print_paper_width: 8.50
     print.printer_IBM_Infoprint_1412_Laser.print_reversed: false
     print.printer_IBM_Infoprint_1412_Laser.print_scaling: 1.00
     print.printer_IBM_Infoprint_1412_Laser.print_shrink_to_fit: true
     print.printer_IBM_Infoprint_1412_Laser.print_to_file: false
     print.printer_IBMLaser1412.print_bgcolor: false
     print.printer_IBMLaser1412.print_bgimages: false
     print.printer_IBMLaser1412.print_command:
     print.printer_IBMLaser1412.print_downloadfonts: false
     print.printer_IBMLaser1412.print_edge_bottom: 0
     print.printer_IBMLaser1412.print_edge_left: 0
     print.printer_IBMLaser1412.print_edge_right: 0
     print.printer_IBMLaser1412.print_edge_top: 0
     print.printer_IBMLaser1412.print_evenpages: true

Server settings look good. Is there a personal firewall or a proxy which might prevent Thunderbird from connecting to the server?

Note, when logging in using OAuth2 the first time you're prompted for your Gmail password in a browser like window. This is your real Gmail password, not any application specific password. After that you're prompted to allow Thunderbird to access Gmail.

That was it. I forgot that when I was away, I had to set my Avast firewall to public. I thought it would have switched itself back to private when it saw that I was home and reconnected to my private home network, but I guess not. Putting it back at private solved the problem. Thanks! Now if I can figure out my POP issue in the other thread I'll be back to normal