I have not been able, so far, to find any references prior to the 1800s to a Latin sentence presenting a dilemma (e.g. aut deus aut homo non bonus – either God or a bad man) that could have been the original basis for the Trilemma. Because of this, I am skeptical that the Latin statement of the dilemma is of medieval or ancient origin. I don’t know the origin of the Trilemma, but I have a plausible hypothesis about how it came to be.

First, a very brief summary of historical apologetics, derived from a book by William Craig (Apologetics: An Introduction; hereafter: AAI). In the 5th century, Augustine defended the authority of scripture based on “empirical signs of credibility, mainly miracle and prophecy.” (AAI, p.130). In the 13th century, Aquinas followed Augustine on this point, but for Aquinas “miracle is the most important sign of credibility.” (AAI, p.130). Jesus’ miracles confirmed his teachings and his divine power. This makes the historical question, “Did Jesus really perform the miracles reported in the Gospels?” of critical importance, but Aquinas “just leaves the historical question unanswered.” (AAI, p.131).

The protestant reformation helped to foster historical consciousness and development of historical methodology, because protestants, especially in the 17th and 18th centuries, made historical arguments that the Catholic Church had departed from the original teachings and practices of the early Christians, and defenders of Catholicism also engaged in historical arguments to refute these protestant objections and to show that the teachings and practices of the Catholic Church were in keeping with those of the early Christians (see AAI, p.132).

The rise of historical consciousness and historical methodology allowed for the development of historical apologetics. According to Craig, “Hugo Grotius was the first to provide a developed historical argument for Christianity in his De veritate religionis christiannae [1627].”(AAI, p.133).

Here is a summary of how Grotius defended the central miracle of the resurrection of Jesus:

…the apostolic testimony to the event of the resurrection can only be denied if the apostles were either lying or sincerely mistaken. But neither of these are reasonable. Therefore, the resurrection must be an historical event.
(AAI, p.135)

Grotius argued for a trilemma about a claim made by the apostles:

(1) One of the following three statements is true:
The apostles were lying about the resurrection of Jesus.
The apostles were sincerely mistaken about the resurrection of Jesus.
The apostles’ claim that Jesus rose from the dead was true.
(2) The apostles were not lying about the resurrection of Jesus.
(3) The apostles were not sincerely mistaken about the resurrection of Jesus.
Therefore:
(4) The apostles’ claim that Jesus rose from the dead was true.
This is the same logic that is used by C.S. Lewis and Josh McDowell in the Trilemma argument for the divinity of Jesus. The person making the claim is Jesus rather than the apostles, and the claim is that Jesus is God, rather than that Jesus rose from the dead, but making those substitutions yeilds the familiar Trilemma argument:

(5) One of the following three statements is true:
Jesus was lying in claiming to be God.
Jesus was sincerely mistaken in claiming to be God.
Jesus’ claim to be God was true.
(6) Jesus was not lying in claiming to be God.
(7) Jesus was not sincerely mistaken in claiming to be God.
Therefore:
(8) Jesus’ claim to be God was true.
So, my hypothesis is that someone following in the footsteps of Hugo Grotius (sometime after 1627) modified his argument for the resurrection into an argument for the divinity of Jesus. Since I have found an early version of the Trilemma that was published in 1733, there is about a 100-year window when the Trilemma argument was invented (1627-1733).