Inquiring minds want to know.
IANAS (I am not a scientist) but I think its pretty light. 
I would imagine it’s as heavy as any other beam of light.
Lightning isn’t strictly light though. It’s the flow of charge from one region to the other, so presumably those electrons have some weight to them. I can imagine a calculation involving the typical charge in a lighting bolt, converting that to the number of electrons and multiplying by the weight of an individual electrons. The details of this calculation is an exercise left to the student 
I wonder if the OP is asking about cause and effect or just the flash we see.
Look for the answer in films of “hot lightning” where the strike lasts for a large fraction of a second. The arc rises upwards, just as it does for a “Jacob’s Ladder” arc. Lightning is lighter than air.
Lightning is not light, and it’s not electricity. It’s plasma. After the current cuts off, the plasma hangs around briefly (or longer in the case of hot lightning.)
Except most of those electrons would be there anyway, right? They’d just be bound up in atoms and molecules, instead of flowing in a big current. So weighing electrons is the wrong concept to use; we might get a better conceptual result from comparing the mass of moving electrons to the mass of mostly-quiescent ones.
A lightning bolt is not a substance or a thing, like a hailstone or something, it’s a name for an event that involves a variety of different materials. You might as well ask “what is the weight of a car accident?”
Says wikipedia, its about five coulombs worth of charge, which is something like 3E-11 kgs. So you probably don’t have to worry about one falling on your head. Or rather, you do, but not because its heavy.
(Kind of a neat example of how large the strength of the electro-magnetic force is compared to the particles that carry it. Such a microscopic bit of charged matter can create something as macroscopic as a lightening bolt).
Charge actually moves from the ground to the clouds, which means that actual charged matter makes a net motion in the same direction. The same electron that leaves the ground probably isn’t one that ends up in the cloud, but at the net effect is that the earth looses 3E-11 kgs, and the cloud gains the same weight, so I think its sensible to call the weight of the electrons transfered the ‘weight’ of a lightening bolt.
Thor might know.
It really depends on what you consider to be part of the lightning bolt. If you just consider it the release of stored electrical energy that the storm generated, then you’re talking about the mass of a relatively small amount of energy. Wikipedia says they average 500 megajoules of energy, or 5e8 J. One milligram of mass is equivalent to around 9e10 J, so you’re looking at that energy having a mass of around a two-hundredth of a milligram.
You could look at it in terms of the mass of the net electron movement. The 5 Coulombs of charge Wikipedia says flows comes from around 3e19 electrons, each of which has a rest mass of around 9e-28 g. So the total mass of the net electron movement is around 2.7e-8 g, or far less than its energy equivalent mass.
But, the net electron movement is tiny compared to the overall mass of the electrons that take part of the energy discharge, so maybe we could figure out the mass of all the particles that take part of the energy discharge. We’d have to ignore the ones that helped create the charge imbalance in the first place, as they aren’t part of the bolt itself. There’s no consensus on the “average” lightning bolt length or width, but I’ll use 5000 m and .01 m as rough estimates based on my quick research. If bolts were square, that’s 1e-4 m^2 * 5e3 m = .5 m^3. A cubic meter of air has about 1.225 kg of mass, so the total mass of the air that participates is around .6 kg, or around 1.3 pounds. Assuming circular bolts, you’d have pi/4 as much, or around 1 pound.
I invite someone checking my math and such.
Of course, the mass of air is mainly in protons and neutrons, with 1/2000 being from electrons. The electrons are the main participants in the movement of the charge, but it’s hard to say that the protons don’t participate at all as they provide the structure around which the electrons move. And then without the neutrons the nuclei containing the protons wouldn’t be stable. So either go with the above calculation, or take 1/2000 of it depending on what you think of what actually constitutes a lightning bolt.