I suppose one of the earliest would be the murder of Bardiya (the younger son of Cyrus the great) in 522 BC.

Murdered by his brother Cambyses II, the unfortunate Bardiya was replaced with a magi known as Gaumata (called 'Smerdis' by Herodotus in his Histories). Gaumata was a magi, possibly a Zoroastrian, and may have used magic to accomplish this feat.

Cambyses II died in 522, from suicide or an accidental wound, leaving an imposter in charge of the Persian empire for seven months. Only a small group of noblemen knew of the switch (because a concubine pulled back his hair and found that 'Smerdis' had no ears, according to Herodotus) and were able to kill the false Bardiya, thus saving the empire.

A stirring tale - and one the eventual successor Darius I would have us believe. So much so that he had it carved in stone at Bisitun.

Herotodus wrote his version eighty years later, Ctesias about forty years after that.

The Greeks took great pleasure in retelling this particular story . At each retelling elements were added or removed and the story grew more fantastical as time passed. A classic conspiracy theory.

(A decent - and short - secondary source is Ancient Persia: A Concise History of the Achaemenid Empire, 550-330 BCE by Matt Waters. Tom Holland also addresses the accession of Darius I in Persian Fire, which is an entertaining read.)

There are a number of ancient conspiracies. Off the top of my head, Livy questions whether the myth that Romulus really ascended to heaven was cover for the fact that Senators killed him and destroyed the body. During the Catilinarian Conspiracy a rumor got out that the reason Caesar objected to summary execution was because he was in on the plot. There is the supposed Baccanalian conspiracy of 186 BCE (Is that date right?), a rumor that Calpurnius Piso was involved in the death of Germanicus, and at least two different impersonators of Nero showed up after his death. And the very well documented conspiracy to assassinate Caesar.

Conspiracy theory, the nutty kind, is a little harder. Nero's accusation that Christians were responsible for the fire in Rome might suit that kind, if you believe Tacitus is right that Nero claimed that.

The Bacchanalian conspiracy I already mentioned seems to have some element of conspiracy to it. The way Livy describes it, it looks like organized crime doing things like forging wills, organized by a religious fraudster.

He was a hedge-priest and wizard, not one of those who imbue men's minds with error by professing to teach their superstitions openly for money, but a hierophant of secret nocturnal mysteries..... When they were heated with wine and the nightly commingling of men and women, those of tender age with their seniors, had extinguished all sense of modesty, debaucheries of every kind commenced; each had pleasures at hand to satisfy the lust he was most prone to. Nor was the mischief confined to the promiscuous intercourse of men and women; false witness, the forging of seals and testaments, and false informations, all proceeded from the same source, as also poisonings and murders of families where the bodies could not even be found for burial. Many crimes were committed by treachery; most by violence, which was kept secret, because the cries of those who were being violated or murdered could not be heard owing to the noise of drums and cymbals.

So there's a religious huckster running around, and some inappropriate fooling around, but notice the list of crimes: perjury, forgery, murder.

To my eyes, the decree the Senate passed about this at the time (it actually exists) looks more like a religious persecution than law enforcement. It limits associations to groups of 5, prevents them from having a common treasury, not to practice ritual without special permission, and bans worshipers from official life.

Livy's conspiracy looks kinda like Jim Bakker's Peter Popoff (oops, got the wrong fraudster) fraud operation, consciously fleecing people under the guise of being a religious leader. The SC version seems to think there is real dangerous religious stuff going on.

I can't think of a "lizard men" type conspiracy better than this. Maybe something will come to me later.

EDIT: to be clear, I realize Livy says the hedge wizard had knowledge of secret mysteries, but people were saying that about Peter Popoff and his faith healing too until James Randi exposed him. Livy's writing some 200 years after this Bacchanalia business and it's clear in his anecdotes about some individuals involved in the cult later that they believed this wizard.

Ronald Syme in The Roman Revolution suggests that there may have been a successful conspiracy for the framing of Augustus' daughter, Julia. The actions she is accused of (getting off with Mark Antony's son) runs counter to every other source of her character, especially those given by Macrobius in Saturnalia in particular. Eliminating the only surviving child of the first emperor was politically advantageous for a lot of people.

I'm not entirely sure if it fits the bill of 'lizard people rule the world' sort of conspiracy, but it may have been a legitimate conspiracy that was acted out by invested parties.

Great question. Sub-question for historians: how would you go about researching this question (with no starting point)?

What would separate a conspiracy theory with traditional mythology, if I could ask a tack on question?

There was the death of Philip II of Macedon, father of Alexander the Great.

The year is 336 BCE. Having pacified and united the Greeks under his hegemony, the cunning and driven Philip II was about to lead a great expedition against the Persian Empire.

Then, attending his daughter Cleopatra's marriage to Alexander of Epirus, he was killed by one of his bodyguards, a man called Pausanias, who was himself killed as he tried to escape, something that seemed a bit suspicious even to contemporaries.

There are a couple of different theories. Diodorus Siculus (through Cleitarchus) says that Pausanias was a jilted lover. This version is very sordid and convoluted, involving Pausanias being set aside by Philip, then taunting Philip's new lover (also called Pausanias) to suicide. Then this younger Pausanias' friend Attalus (the new queen's powerful uncle) decided to take revenge by getting the older Pausanias drunk and gang-raping him. Pausanias' beef with Philip was with the fact that Philip did not punish Attalus.

Justin (another historian) points the finger at Olympias, Alexander's mother. Philip's new wife had just given birth to a new son, which would have severely jeopardized Alexander's succession given their strained relationship at the time. If Olympias was innocent, she certainly didn't act like it. For example, she dedicated to Apollo the sword Pausanias used to murder Philip.

So was Philip II's death a crime of passion, or calculated political assassination?

Related question: how old is the blood libel? Any sense of its specific origins?