Leaky Paywall uses the built in wp_mail php function. If all other WP emails (password resets etc) are coming through then it’s probably a spam filter on the subscriber end.
You can try installing an email log plugin which will show you every email that is sent via WordPress on your site, including Leaky Paywall new subscriber emails. You can then check the email log to see if your site is sending the new subscriber email and which user they are being sent to. If the user is not receiving them in their inbox, have them check their spam folder.
You may need to set up an SMTP plugin and use a service like Mailgun and let it send the emails for you. Its not the plugin itself, but that your site’s server isn’t “optimized” to deliver transnational emails. Here’s an article about the why and how. Its about it with Ninja Forms, but the same principles apply. Emails Not Working