The following is a response I posted in the Mozilla support site regarding the changes Google have announced revoking the use of "less secure apps" effective the 30th of may according to the emails they send me. Hopefully I will have time to codify it in a support article, but until then this will have to do so I can find it again.
Go to account setting on the menu
Then select the server settings for the account you wish to change.
Change the Authentication method using the drop-down to oAuth2 like shown below
Follow that up by selecting the outgoing server SMTP entry on the accounts list.
This will display all configured SMTP servers something like this.
Select your outgoing server, press the edit button on the right. Then edit your authentication to oAuth as shown in the image.
