E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Horns of a Dilemma.
A difficulty of such a nature that whatever way you attack it you encounter an equal amount of disagreeables. Macbeth, after the murder of Duncan, was in a strait between two evils. If he allowed Banquo to live, he had reason to believe that Banquo would supplant him; if, on the other hand, he resolved to keep the crown for which he had filed his hands, he must step further in blood, and cut Banquo off.
Lemma is something that has been proved, and being so is assumed as an axiom. It is from the Greek word lambano (I assume or take for granted). Di-lemma is a double lemma, or two-edged sword which strikes either way. The horns of a dilemma is a figure of speech taken from a bull, which tosses with either of his horns.
Teach me to plead, said a young rhetorician to a sophist, and I will pay you when I gain a cause. The master sued for payment at once, and the scholar pleaded, If I gain my cause you must pay me, and if I lose it I am not bound to pay you by the terms of our contract. The master pleaded, If you gain you must pay me by the terms of the agreement, and if you lose the court will compel you to pay me.