Yes, using LoRa radios to receive messages is possible. For the Arduino platform, the LMIC library can be used. See my code for mobile node with gps and gateway. The gateway publishes data to a service called PubNub, which has a free tier that probably is sufficient for your needs.
It should be fairly easy to modify the gateway code to send data to your own server if you prefer that.
However, I suggest you consider LoRaWAN anyway. The Things Network (TTN) is a free LoRaWAN service. Check their map if they have coverage in the area you are interested in. I have used the relatively cheap RFM95W radio module to send messages to TTN using the LMIC library. The library's example code will get you very far.
The upside with TTN is that you might not need to set up your own gateways, and you can use their coverage throughout the world. If TTN does not have coverage in the area you need, consider building/purchasing a gateway and connect it to TTN. That way you add to their coverage and can still use their other gateways. A LoRaWAN gateway is much more expensive than a single radio though, they start at about 250 USD.
Full disclosure: I use, but am otherwise not affiliated with LoRa, TheThingsNetwork, LMIC or PubNub.