Please go to your Settings and then to Notification Settings. There you can activate/deactivate the options in question by swiping over the button.
In order to allow push notifications in general:
1) Make also sure that your iPhone settings allow push notifications. You find this setting under Settings / Notifications and then under Lifesum / Notifications.
2) See also to it that you are allowing Settings/General/Background App Refresh on your iPhone
Please note: when you use an Apple Watch and your phone the notification will appear on the device that is unlocked.
To get to the Settings click on the three small dots to the right on the tab bar at the bottom of the screen and click on Settings in the list of the menu. Then click on Notification Settings. There you can activate/deactivate the options in question by swiping over the button. Make also sure that your phone settings allow push notifications. You find the settings under Settings / Sound & notification and then under App notifications / Lifesum.