In order to receive instant D2L Discussion notifications via email, you need to subscribe to Discussion Forums and Topics in the Discussions area of a course, and apply the appropriate Instant Notification settings in the Notifications area of your D2L profile. It is likely that you have not yet applied the necessary Instant Notification settings in the Notifications area of your D2L profile.
You can find detailed instructions for subscribing to Discussions and applying the necessary Instant Notification settings within the “Subscribe to Discussion Forum or Topic” section of our D2L Discussions guide.