Wunderlist Notifications?

did you tried update this list (as root) and restart lipstick?:
/usr/share/lipstick/androidnotificationpriorities
And also apply to run in background: Settings->Apps->YOUR-APP.

Yes it is set to run in the background. Regarding your first point, I would need to add the package details for Wunderlist (and any other Android apps I wanted to use) to the 'androidnotificationpriorities' file would I? Is this relatively easy, I'm afraid I'm not a developer! Apologies if I'm wasting your time and don't really belong here without those skills-keen to learn though! Thank you.

It's not so hard... If you want to try, follow this instruction:
Open terminal as ROOT and write (all commands here is a one-line command, just copy-paste):

systemctl status aliendalvik

It will show you android processes, for example for skype, you will see com.skype.raider, for WhatsApp you will see com.whatsapp. Remember name of process of your app.
Create a copy of androidnotificationpriorities file.

/bin/cp -f /usr/share/lipstick/androidnotificationpriorities /usr/share/lipstick/androidnotificationpriorities.orig

Add your app to the list. This is one-line command, just copy-paste it (change APP_NAME to name of your app, for ex: Wunderlist, and APP_PROCESS to process of your app, for ex: com.wunderlist):

echo "
APP_NAME;chat,chat_exists
package:APP_PROCESS;chat,chat_exists" >> /usr/share/lipstick/androidnotificationpriorities

Restart lipstick (homescreen):

systemctl-user restart lipstick

Open your app, create task that should send notification. Close your app and see if it send notification at time that it should send.

To restore the original list:

/bin/mv -f /usr/share/lipstick/androidnotificationpriorities.orig /usr/share/lipstick/androidnotificationpriorities

And restart lipstick (homescreen):

systemctl-user restart lipstick

That all ;)

If it work like you expect, I can add this app to my Android app notification: https://openrepos.net/content/schturman/android-apps-notifications

Thanks for this, I have followed these excellent instructions and the following entry now appears in the lipstick/androidnotificationprioroties

Wunderlist;chat,chat_exists package:com.wunderkinder.wunderlistandroid;chat,chat_exists

Unfortunately I still don't have any notifications. The app is definitely set to run background processes at boot up. I wonder if the presence of the 'Android Notifications' app from Coderus might be messing this up? Thank you!

I don't know, I don't use it since jolla implemented this way of android notifications. Also problem may related to android app itself and app can't send notification if not opened... Don't know, just play with it...