Archimedes' Lever is the Storm King. Forged by master-Spark Van Rijn, along with being powerfully electrified in some fashion, it was "bound to its owner's soul", allowing him to sense and activate it from (at least) a fair distance away. According to Violetta, the blade was also sharp enough to "cut the day out of the night", whatever that means.wielded by the original
The Jägermonsters refer to it as Slasher.
The Storm King was somehow physically separated from the weapon before disappearing from the historical scene (by Van Rijn, if Andronicus is to be Agatha's era, it is in the possession of Storm-King descendant Tweedle in Paris. When it is reactivated by Adronicus's being freed from his temporal prison, Tweedle Sparkily attempts to break its connection with its former(ish) owner and then use it against him. It works to the extent that Tweedle is able to part way into the Storm King's remaining weapon, The Platonic Solid. However, to pretty much universal non-surprise, when Tweedle later attempts to run Andronicus through with the sword, the Storm King beats off the attack and the blade.); when first seen in
Simon Voltaire, the Master of Paris, then resumes his fight against Andronicus, whereupon he channels all the available energy in Paris into one massive blast of power tuned to the Lever and the Solid, both into slag.
Possibly relevant outside information
The sword's name is a reference to a quote from the ancient Greek philosopher-scientist-Spark Archimedes: "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world."