This is a reference to Dionysios I of Syracuse, who was tyrant in the 4th century BC.

The life of a tyrant was apparently admired by some in antiquity for its outward splendor, absolute and unquestioned power having its advantages. But it was also frequently stated among philosophers and other writers that the actual life of a tyrant is one dominated primarily by fear: they are constantly afraid that someone will kill them, either to eradicate the tyranny or to become tyrant themselves. Some tyrants went to extreme lengths to avoid assassination and made themselves ridiculous. Plutarch says of one petty tyrant (Life of Aratus):

Then he would lock the doors of the inner house, and betake himself with his mistress to a little upper room, which was closed by a trap-door; on this door he would place his couch and sleep, as one in his state of mind would naturally sleep, by fits and starts and in great fear. The ladder the mother of his mistress would take away and lock up in another room, and in the morning would put it in place again and call the wonderful tyrant, who would come down like a creeping thing out of its hole.

Of Dionysios himself, our tyrant, Plutarch says in the Life of Dion:

For the elder Dionysius was so distrustful and suspicious towards every body, and his fear led him to be so much on his guard, that he would not even have his hair cut with barbers' scissors, but a hairdresser would come and singe his locks with a live coal. Neither his brother nor his son could visit him in his apartment wearing any clothes they pleased, but every one had to take off his own apparel before entering and put on another, after the guards had seen him stripped. And once, when his brother Leptines was describing to him the nature of a place, and drew the plan of it on the ground with a spear which he took from one of his body-guards, he was extremely angry with him, and had the man who gave him the spear put to death. He used to say, too, that he was on his guard against his friends who were men of sense, because he knew that they would rather be tyrants than subjects of a tyrant.

So there was a strong literary tradition that tyrants live with constant fear and apprehension.

In this context, the story about Damocles is told most famously by Cicero in Tusculan Disputations 5, which is where Martin Luther will have read it:

Indeed this tyrant himself gave his judgment as to how fortunate he was. For when one of his flatterers, Damocles, mentioned in conversation the wealth of Dionysius, the majesty of his rule, the abundance of his possessions, the magnificence of the royal palace and denied that there had ever been anyone more fortunate, he said, "So, Damocles, since this life delights you, do you wish to taste it yourself and make trial of my fortune?"

When Damocles said that he desired this, Dionysius gave orders that the man be placed on a golden couch covered with a most beautiful woven rug, embroidered with splendid works; he adorned many sideboards with chased silver and gold; then he gave orders that chosen boys of outstanding beauty should stand by his table and that they, watching for a sign from Damocles, should attentively wait on him; there were unguents and garlands; perfumes were burning; tables were piled up with the most select foods. Damocles seemed to himself fortunate.

In the middle of this luxury Dionysius ordered that a shining sword, fastened from the ceiling by a horse-hair, be let down so that it hung over the neck of that fortunate man. And so he looked neither at those handsome waiters nor the wonderful silver work, nor did he stretch his hand to the table. Now the very wreaths slipped off. Finally he begged the tyrant that he should be allowed to depart because he no longer wanted to be fortunate.