There is no such thing as "tesla energy".
The "Tesla" is, however, a unit used to measure the strength of a magnetic field.
Magnetic fields are tough to use as weapons because a) they really don't bother people very much, and b) they are strongest where the source of the field is, and they drop off in intensity according to the inverse cube law. There's no way we know of to "project" a magnetic field for a long distance. Even if we could it would still be far stronger at the source than at the target. So to the extent that the magnetic field did bother people or interfere with weapons, it will affect the "shooter" a lot more than the enemy. (Also known as "shooting yourself in the foot.")
Magnetic fields don't make lightning. Static electric charges make lightning. We can "make lightning" on a small scale with a variety of types of electrical apparatus, but nowhere close to the distance or intensity of the real thing. We don't know for certain where the enormous static charge buildups that cause lightning come from but we're quite certain magnetic fields aren't the cause - we can measure magnetic fields very well and we've never seen them leading up to a lightning discharge.
Of course, when the lightning does "fire", the enormous current (ca. a million amps) does create a strong magnetic field for an instant... and this is the cause of a lot of the damage from lightning in buildings and wiring and so on that isnt struck directly... but that's the lightning causing the magnetic field, not the other way around.
Note that the "lightning" from a Tesla coil is not really the same thing as lightning in nature - it's generated by high-frequency alternating current, while lightning in nature is static electricity, a "direct current" phenomenon.
One other point: While a brilliant inventor in his early years, Tesla later deteriorated into more or less a loon. His "wireless power transmission" system could not possibly have worked at a practical level (efficiency would have been about 0.000001%); his particle beam weapon could not have worked at even moderate distances, far below the range where much simpler, already existing gunnery worked just fine.
He was fascinated by resonance, but completely missed the point (or disbelieved) that resonance creates no new energy. In particular his ideas about his little mechanical oscillator that supposedly could fell buildings and even split the earth conveniently ignored the phenomenon, already well known at the time, of "damping".
His later life is marked by a long series of amazing claims that were never demonstrated. While a brilliant experimenter he was not much of a theoretician - at various times he dismissed the Bohr atom, Maxwell's equations, Einstein's relativity theory, and the possibility of nuclear energy as so much nonsense.
This is not to take away from his real achievements: The AC induction motor and generator, three-phase AC power generation and distribution, the Tesla turbine (which was only about half as efficient as he claimed, and useful only in very specialized applications, but still a worthy achievement), some development applicable to early radio and even radio remote control. But all of these were comparatively early. If only he'd been a bit smarter about licensing his patents to Westinghouse, and then quit while he was ahead...
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