The mobile phones you have will do this all just fine on their own.
Not without a GSM or WiFi network available.
Another important feature of this project is to avoid interference, so some sort of unique device ID that let's communicate two groups of devices in a completely separate way, an example to clarify:
If by "interference" you mean having your messages read by the other team... Just use some simple encryption. Each team has an encryption key they share only among themselves. Each message has a team ID. If someone tries to read a different team's messages they will just get the encrypted version.
But I think that this can be implemented with some kind of setting for LoRa (by the way, I looked and it seems it's the right module for this project as you all suggested).