Evidence Found Of Lightning On Mars
This link does not mention about how they have detected the lighting on Mars.

http://www.ns.umich.edu/htdocs/releases/story.php?id=7199

It's still pretty early this morning, but as to detection methods for such interesting discharges, I note the article used the term 'huge'. Perhaps the discharges were seen in night side images of dust storms ?? Or, could such discharges be noted in DSN receivers while monitoring Mars orbiting craft if the geometry was right ??

Soviet era Venus craft had a device called 'Groza' to detect lightning strikes, I am not sure a specific analog to this device has been flown by US craft to Mars.

According to the link above it's from a microwave instrument, presumably earth-based (?)

Hard to interpret this. A 'kurtosis detector' seems to imply that it's looking for sudden peaks in emission rather than a normal distribution across the monitored spectrum, which maybe is why they describe it as distinguishing thermal vs. non-thermal (non-blackbody radiation).

That's my best guess, anyhow, and it does seem to be an Earth-based instrument. The article definitely could have provided a better description.