LR Email problem:Failed to establish connection with the outgoing email server.

Had the same problem and it was in fact related to 2-factor authentication. 

I went to Google account settings_Sign in & Security_Password & sign-in method_App passwords

App passwords let you sign in to your Google Account from apps on devices that don't support 2-Step Verification. You'll only need to enter it once so you don't need to remember it.

Select App: Choose "Other (Custom name)

Give name: "Lightroom" and click Generate

Copy that password into Lightroom. Click Validate and see if validates.

It worked for me at least.

Do you use the 2 Step authentication system in Gmail? If you do you will need to give LR an Exception to that. You do that on the Gmail options/settings system.

Also change smtp.gmail.com to smtp.googlemail.com

Not sure if that is the problem or not but that is how it is setup in my desktop mail program.

And connection security to SSL/TLS