There is lightning on Mars! Or at least, something like lightning occurs on Mars. In 2009, the first detections of lightning strikes on Mars were recorded, confirming something that planetary scientists had suspected already - electricity should arc through the Martian skies.
We knew a fair amount about Mars’ weather patterns even before detecting lightning, from a combination of orbiting spacecraft and our landers on the surface. These outposts have painted a picture of a thin atmosphere frequently tumbled into large dust storms. Mars has huge annual storms which can envelop the entire planet, and other strong storms that pop up irregularly through the year. On top of that, the dust on Mars is extremely fine, so once you begin to swirl it around in a wind, it’s reasonable to guess that the dust particles will start to rub on each other, and as you do that, you’ll start to build up an electric charge.
This static charge does more than just gradually build towards lightning; it’s also part of why the Mars rovers get so dirty. The rovers are dealing with more than just a fine sifting of dust falling out of the atmosphere, which a light breeze might easily remove; that dust is stuck to them like packing peanuts stick to your hands. It takes a stronger breeze - a new storm, or a wandering dust devil - to remove some of that dust, and it’s something that the long-lived Spirit and Opportunity rovers were both able to make use of on a couple of occasions.
However, as much as dust devils can help you out, they can also do the opposite, dumping more dust on top of your solar panels, which, for a solar powered craft, will limit the amount of energy you have available to do science with, and eventually drop the craft below the threshold of power it needs to operate. This is the current theory for what happened with both Spirit and Opportunity. The Curiosity rover is less affected by this particular issue since its power comes from radioactive decay, but Curiosity is still fully coated in the fine Martial soil. This dust is actually a concern for human exploration of Mars - it’s going to be hard to fully remove this dust from spacesuits, and breathing in a fine particulate is never good for your lungs.
The lightning itself is actually less likely to be a hazard to astronauts on the surface of Mars than the dust is; for one I would expect any humans on the surface of Mars to take shelter during these bigger storms. Unlike what was presented in The Martian, even the 60 mph winds that can occur during a dust storm wouldn’t feel as powerful as a similar wind on Earth, since the atmosphere is so much thinner. The air simply wouldn’t exert the same pressure against you in the same way. Even on Earth, the likelihood of being struck by lightning is very low, and on Mars the best guess is that the lightning would not really resemble the large bolts of lightning we see here on Earth.
More likely is that this lightning would resemble the arcing jolts of electricity you can create by shuffling along in socks on carpet and then touching a doorknob. In a dark room, you can see the filamentary discharge of electricity between your finger and the doorknob. On Mars, you might expect to see little flickers of electricity arcing between parts of the dust storm, faintly lighting up the night sky. To be a hazard to an astronaut or a rover, you’d have to be very, very unlucky.