Well you will need internet access to download and install anything. However you can do this over WiFi anywhere and don't have to have even a phone plan to do so. I have an old Android phone I kept that I have no service on, but can turn on my home WiFi (or go anywhere where I have WiFi access even) and download things to the phone.
Once you have access, you can easily download many apps. I would suggest downloading the "NextRadio" app, which I am not sure if that is the one that came on that phone or not, but it seems likely unless LG had its own app.
You should be able to find it on the Google Play Store, or you can get it here... http/nextradioapp.com/