An allegator is an alleger, someone who alleges, who claims something to be true, especially if the claim lacks proof.
Allegator comes from a synonym of allege: to allegate. The latter rarely rises to the surface of conversation but it does exist. It has an interesting agent noun, allegator, that indicates the doer of the deed. Even if it is rarer than alleger, it certainly has more potential for play, given its homophone, alligator.
Now, when you are subjected to false allegations, you have a more emotionally charged word for your accusers: "Ben Downe is nothing but a cold-blooded allegator who made up the whole story about me putting the frog in the water cooler." How's that for an image of your accuser? Around the house? Sure: "Mom, I am not picking on Billy; he is just an irresponsible allegator." Now, doesn't this word cast a much more powerful beam than liar?
This word is a creation from Latin allegat(us), the past participle of the verb allegare "to send off, relate, recount." The verb comprises ad- "(up)to" + legare "to appoint, assign." So, the prefix al- here is really ad-, whose consonant assimilates to any other consonant to which it is attached (arrest, attest, adduce also contain a hidden ad-). The primitive root, *leg-/log-, gave us Latin lex, legis "law" and Greek logos "speech, word, idea." The best guess as to how these two meanings crossed paths is that this root goes back to the day when a king's word was the law.