Just to be the devils advocate, I'm going to say the guy with the lightsaber wins more often than the gunman

I'm going to say the guy bringing a gun to the sword fight wins

Mythbusters proved that myth is not entirely accurate, depending on the scenario. I think 3 meters is close enough to at least pose a threat.

The gun-wielder has fired the gun before, and is reasonably proficient with it (But not an expert marksman or anything)

Being proficient on the gun range doesn't necessarily mean that a person is proficient in real life. Here is where I get this information from. A quote from the article

In the real world, people aren't as cool and accurate when shooting something that isn't an unmoving piece of paper. To be specific, after studying more than 200 violent encounters, no connection whatsoever has been found between prowess on the range and effectiveness in combat. None. Hollywood taught you that the pistol-armed guy hitting the bull's-eye at 90 feet at the gun range is a champion badass, but science says that's bullshit

Although I will say that 3 meters is definitely close enough range for the shooter to be accurate.

Without the Force to assist, the lightsaber is all but impossible to wield effectively. He goes down immediately and doesn't get back up.

I mean, Lightsabers are lightweight, and can easily cut through most things in our world with a slice. I don't think there would be a problem cutting or stabbing someone with it when it goes through people like butter. Especially if the person is trained with a sword. Hell, even younglings can weild them, and so was Luke before being trained in the ways of the force

And also you have to consider where the person would be shot. Humans do not automatically die from bullets like they do in movies. Unless if the swordsman is shot in the face or in the hand (the hand that he is holding the lightsaber with) before he is able to reach his opponent, then the swordsman should likely be able to deal a lethal blow (I would consider having your body chopped in half more lethal than a bullet or two to the chest).

IMO the most likely scenario is that both characters are able to hit each other with their respective weapons, but the swordsman is more likely to survive the encounter because there is a greater chance for a human to survive being hit by a bullet than there is being cut half by a lightsaber.