Even when you were in "do not disturb" mode, your phone can still receive notifications, but in a silent way, so LunaR APP can still "read" it. 

If you don't want to be disturbed with watch vibration, you can turn off watch BT by long pressing (2 secs) the right button. To turn it on, press any button is fine.

Or, on LunaR--Settings--Permission, "Turn off Push Notifications". You won't receive any notification.