John Boswell ("Same Sex Unions in Pre-Modern Europe") names Polyeuctus and Nearchus as one of the three primary pairs of same sex lovers in the early church. (The others are Sergius & Bacchus and Felicity and Perpetua). Other sources are less certain that they were lovers: the useful "God is Wonderful in His Saints" Orthodox Resources website describes them simply as "friends". Before dismissing Boswell's claim though, we should remember that "friends" has sometimes served as a euphemism for "lovers", just as to "sleep with" someone in modern English usually means more than to share a snooze.
"Polyeuctus and Nearchus were fellow-officers and close friends, serving in the Roman army at Miletene in Armenia. Nearchus was a Christian. Polyeuctus, though abundant in virtues, was still imprisoned in idol- worship. When the Emperor Decius' persecution broke out (239-251), an edict was issued requiring all soldiers to show their loyalty by making public sacrifice to the gods. Nearchus sadly told Polyeuctus that because of the decree they would soon be parted. But Polyeuctus, who had learned about the Christian faith from his friend, answered that Christ had appeared to him in a vision, exchanging his military uniform for a shining garment and giving him a winged horse. Polyeuctus took the vision as a sign that he was to embrace the Faith, and that he, with Nearchus, would soon be lifted up to heaven. Almost immediately, he first tore down the Emperor's edict in front of a startled crowd, then smashed the idols being carried in a pagan procession. He was quickly arrested and subjected to beating and scourging for sacrilege, but he only proclaimed more forcefully that he was a Christian. When the persecutors saw that Polyeuctus' patient endurance was bringing other idolaters to the faith, they condemned him to death."
Boswell, John, Same Sex Unions, 141-44