Hi all, thanks for the replies!
noiasca:
if you are looking for a small footprint, (nearly) ready to go solution, consider the TTGO LoRa32 http://s.click.aliexpress.com/e/c8lG1lyy - which brings MCU, LoRa and a Oled on board. Add two wires, connect power, upload sketch - works.
Thanks I've seen a few of these boards but they're expensive and I don't really need any of the extras they have.
jgromes:
I've used SX1278 LoRa modules with Pro Mini without any issues, your problem with receiver not working is probably not due to power issues. Though it's hard to guess without schematic and code.
Wait a minute..I am currently trying with a Nano board (and wasn't expecting it to work at all, but the transmitter does work and I don't know why). Check my reply to @srnet below. Using standard sender/receiver code from LoRa examples and connections from here
jgromes:
As per 2: you might be confusing power voltage level and logic levels. Most SX1278 modules don't have built-in level shifters, so I highly recommend using those if you want to use board with 5V voltage. No need for level shifting with 3.3V with Pro Mini though.
That's what I was saying
If I use a level shifter to shift Nano's 5V to 3.3V and use that to pwoer the LoRa module, would it work? Basically the Nano (if I remember correctly) outputs around 50mA on the 3.3V pin..but what about the 5V pin? Does it output the same mA?
srnet:
A 3.3V Pro Mini will drive a SX1278 SPI LoRa module just fine.
Ok thank you. I was also checking the Pro Micro because it has the built in usb which would make it easier for me to manage. However it has 32U4 chip and I can't find the output power for the 3.3V pin in the schematics (it says Max current output 500mA). Do you think this board would work too with the LoRa module?
srnet:
How do you know the transmitter is working and the receiver is not working ?
So, I've tried the following combinations:
Nano 328P (TRANS) -> UNO (REC) = it seems to be working fine with the exception that messages are printed twice in the received (as if they were received twice) and haven't four out why (yet)
Nano 328P (TRANS) -> Nano 328P (REC) = no errors on either side but receiver will only print out the first few messages after pressing reset button (assuming a delay(10) in the transmitter's code).
therefore I assumed the transmitter is working fine (since I haven't had any issues with it) and the receiver was not (since it only works with the UNO).
However I was just trying (knowing that Nano boards don't work). So after all my question now is only if the Micro Pro would work or if I should just go with the Pro Mini (but then I'd need the USB cabling too)
Thanks! 
L.