How is the speed of electricity determined? Before I am told this is a duplicate, I'd like to be specific here. I have searched online for an answer regarding the speed of electricity in general and haven't found what I'm looking for. Even in this part of Stack Exchange I haven't been content with the responses.
I might be told about drift velocity or electromagnetic propagation. The former isn't what I am looking for, or at least it hasn't been presented to determine what I'm looking for. I'm not interested in the velocity of an electron in copper wire. If I see lightning or electricity from a Tesla coil, I see speeds far greater than what I'm told about an electron in copper wire.
I am aware of an electron avalanche, but I have no idea how that is meant to explain how fast lightning or electricity travel. I'm not sure about EM propagation, either. That seems to be different from what I am looking for.
 A: I think the fundamental problem is that "electricity" as you describe it, doesn't actually exist.  The word "electricity" has many separate and contradictory definitions, so it cannot serve as a useful term in physics.
Analogy: if you were asking about the "speed of optics," nobody could answer, since the word "optics" could mean several completely separate things.  The speed of falling lenses?  :)  To ask a meaningful question, ask about the speed of lenses, or perhaps the speed of light, and avoid the word "optics."
In a similar way, the word "electricity" lacks any narrow scientific definition.  No single "electricity" exists.  The word is commonly used to refer to propagating electromagnetic energy along wires (which moves at nearly the speed of light.) But "speed of electricity" also refers to the flow of charges during electric current (which drift along at centimeters per minute and less.)  The word can also mean any electrical phenomena: wires are electricity, sparks are electricity, batteries are electricity (but transistors aren't electricity, instead they're electronics.  See, confusing!)
In other words, sparks aren't made out of "electricity," any more than lenses are made out of "optics," or bicycle gears are made out of "physics."  To ask a sensible question, avoid the word "electricity," since it has multiple contradictory meanings.
Speed of electrical energy: roughly the speed of light, but lower than c because of refractive index of cables' dielectric.
Speed of electric current: very slow "drift velocity" of charge carriers, but it's proportional to the current, conductor size (sectional area,) and to the carrier density (e.g. metal versus salt water versus electron beams.)  High current gives fast carrier-drift, and at zero current the charge-carriers come to a halt.
What is the speed of leaping sparks?  Sparks are an example of electrical plasma, also called "plasma streamers." The speed of a visibly-leaping spark is the speed of tip-growth of a plasma streamer.  When a plasma-streamer extends itself, the plasma isn't moving along.  Instead the nitrogen and oxygen in the air ahead of the spark is being converted into plasma, which adds to the tip of the growing leader.  Lightning is a progressive converting of air into plasma.  In other words, lightning is actually a "lichtenberg figure" made of nitrogen-oxygen, rather than being made of damp wood.  These wood-fractals are made by converting insulating wood into conductive carbon paths, while lightning is the converting the insulating air into conductive plasma paths.
Such growth can have many different speeds, from zero speed of non-growing coronas displayed by Jacob's Ladders and by tiny Tesla coils, to the easily visible growth of Anvil Crawler lightning, to the extremely rapid propagation of "stepped leaders" in a larger lightning discharge.
See examples both of stepped and continuous lightning leaders, 9,000FPS video:
https://www.youtube.com/watch?v=4q6gHWN8fDE
https://www.youtube.com/watch?v=Q6h9jfURJ6Q
Or, see "anvil crawler" lightning patterns spreading relatively slowly across a horizontal storm-base:
https://www.youtube.com/watch?v=Y5CzaVctGWg&t=1s
A: The "speed of a lightning strike" is the speed that the electric field propagates in air. A potential difference is established between the clouds and the ground, and this potential difference increases dramatically. Paths of ionized air are created between the clouds and the ground. When these paths make a connection between the clouds and the ground you get a discharge that you see as lightning. The great flash you see is not motion of electrons however. This connection allows the transfer of electrical energy, and the effects of this energy transfer (ionization of the air in the connection between the ground and the clouds into a very bright plasma) move at whatever the speed of propagation of light is in air since photons are responsible for the electromagnetic force. This process is the same in wires. Once you connect a light bulb to a battery, the electrical energy is transferred from the battery to the bulb at whatever the speed of light is in the wire. 
Electron drift velocity is also due to the application of an electric field. However electrons do not move in a wire at the speed of the electric field in the wire. Before a field is applied, electrons move randomly within the material. When a field is applied, this random movement is given a direction, but its magnitude is usually very small and depends on many factors. From Wikipedia, the drift velocity $u$ is
$$
u=\frac{m\sigma\Delta V}{\rho efl},
$$
where $m$ is the molecular mass of the metal, in kg; $\Delta V$ is the voltage applied across the conductor, in V; $\rho$ is the density (mass per unit volume) of the conductor, in $\text{kg}/\text{m}^3$; $e$ is the elementary charge, in C; $f$ is the number of free electrons per atom; $l$ is the length of the conductor, in m; $\sigma$ is the electric conductivity of the medium at the temperature considered, in S/m.
So to summarize and perhaps be clearer, the only "speeds" that exist in this case are electromagnetic propagation and drift velocity. The reason why lightning is so fast is because you're seeing the effects of the electric field propagating through air. What follows is very informal but perhaps more digestible. The units for electric field strength are V/m, so if you consider the massive potential difference, or voltage, between the clouds and ground you can glean that the magnitude of the electric field between them is massive as well. This field strength reaches the point where electrons can be stripped off atoms to create plasmas, and it is this stripping of electrons from atoms that occurs at the speed of light in air (in succession between the clouds and ground in the connection established from paths of ionized air in the first paragraph). This ionization gives off visible photons. Intuitively one connects in one's mind the flash of lightning as being a result of electrons moving, but is in fact not due to electron motion at all.
Edit: I say "speed of light in the wire/path" a lot here, but physically there is no electric field inside of conductors so no propagation occurs on the inside. Thanks to @andars for pointing this out.
