No, your LibreLinkUp app* does not need to be open or running to get notifications†‡ if you’ve opened and signed into the app at least once.
* Check the support section of www.librelinkup.com for information about mobile device and operating system compatibility. LibreLinkUp is not intended to be used for dosing decisions or to replace self-monitoring practices as advised by a physician and requires registration with LibreView.
† The user's device must have internet connectivity for glucose data to automatically upload to LibreView and to transfer to connected LibreLinkUp app users.
‡ Alarm notifications will only be received when alarms settings are enabled and turned on and sensor is within 20 feet (FreeStyle Libre 2) or 33 feet (FreeStyle Libre 3) unobstructed of the reading device.