If you are not able to reset your password from your custom WordPress site, maybe your PHP is not able to send mail via phpmail() function. In this case setting up a SMTP is a good solution.
Google provide a free SMTP service with up to 2000 mails in every day. That’s sounds very good but in order to setup SMTP you need to activate your less secure option. And in this post I tell you how less secure option work. And security problem with less secure apps.
Google Less Secure Apps
According google’s official help center, if any app doesn’t meet google’s latest security standard, then you need a less secure option in order to connect with google servers. That means your server sent directly password to google for authentication. Which is seriously security problem with your google password. Any body can retrieve your password directly. And maybe your google account can hacked.