The lightning gun fires, essentially, a basic laser rifle's laser. At the point of impact it generates a natural gas cloud. After a moment, a second laser flies in (horizontally, from a seemingly arbitrary location) towards the gas cloud to ignite it. The secondary laser might not be able to reach the gas cloud (blocked by terrain/objects) in which case the gas cloud can be ignited manually by firing another shot into it (with the lightning gun or any other weapon that can ignite natural gas).
If the target is killed by the second laser or the ignition of the natural gas cloud, perks like Contract Killer and Lawbringer will not be activated (since you didn't actually kill the target).
Firing this weapon can potentially damage the player, depending on proximity.
On occasion, the weapon will glitch, and continuously spawn natural gas clouds at the point of impact for every frame leading up to the second laser's detonation, creating a massive flame capable of extreme damage accompanied by a massive bright flash and a buzzing blast sound, though briefly bringing the game's framerate to a near standstill for a few seconds depending on the system. On weaker PCs, this may lead to a game crash.
Firing the weapon at a spot somewhat far away may often not spawn the gas cloud, unless it strikes an enemy. The secondary laser will still fire.
The name "Lightning Gun" does not seem to fit with the weapon's qualities - neither the initial laser nor the secondary laser resemble lightning. It is possible that the secondary laser was supposed to represent lightning, thus the name.