There are several levels of settings involved to successfully receive notifications from your iPhone to your Lezyne GPS device.
First, open your Lezyne Ally v2 app and navigate to the More tab. Then, select App Settings.
Toggle on Notifications.
It's not clear exactly which apps Apple separates into which of these categories. That might take some experimentation on your part to make sure you're getting exactly the notifications that you'd like.
Your Phone's Settings
Now, let's go into your settings on your iPhone.
Scroll down and select Notifications.
Here you will see all of your apps. Select an app that you want to receive notifications from.
Lock Screen, Notification Center, and Banners all have to be turned on, and Banner Style set to Persistent.
If this doesn't result in you receiving all of the desired notifications, check out the phone pairing article.
Note: Your phone does have to be locked for the text to come through. The phone only sends the notification to the GPS device if it thinks you haven't seen it.