Dio and Lucciola are both male and definitely share a special relationship, but they're not in any kind of romantic or physical relationship.
To wit, Dio and Lucciola were friends as children growing up. This continued until they reached maturity. In fact, Dio holds Lucciola in such high regard that...
Even after Dio is initially brainwashed by the guild (and Lucciola snaps him out of it by effectively sacrificing himself before Delphine), when he realizes that Lucciola is dead, he keeps the rear seat of his Vespa empty out of respect of the memory of his fallen comrade. (Note that initially Dio demanded it stay empty because he was still a little distraught behind the loss of his friend. He somewhat mellows out in Fam, the Silver Wing.)
However, make no mistake:
- They're both male,
- They're not romantically involved, and
- They were definitely close friends.
You don't have to be sexually attracted to someone to have a close relationship with them.