User blog comment:B214/Question and Answers/@comment-50.11.177.49-20130502005857/@comment-33447191-20130502012902

Well it's only a theory but I'm guessing that since they were both from the House of Lucifuge, otherwise known as  a family of Pure-Blooded Devils  from the Extra Demons whose family served under the original Lucifer, so by that logic,  Grayfia was originally from the Old Satan Faction that opposed the Anti-Satan Faction. Sirzechs Lucifer was the  ace of the Anti-Satan Faction alongside Ajuka and was even called a Hero. However, the two fell deeply in love so much that t heir romance became a well-known romantic story among the young Devils and was even made into a movie. The two of them married each other after the end of the conflict between the Old Satan Faction and the Anti Satan Faction, eventually giving birth to a son who you know as Millicas Gremory. Needless to say, Euclid Lucifuge was pissed off that his own sister of his own blood would marry that "fraud of a Lucifer", and adding insult to injury, leave their side and have a child with him. I'm guessing afterwards he joined the  Old Satan Faction of Khaos Brigade and is now plotting his revenge.

As for the relationship between Sirzechs and Euclid, not sure just know that Euclid despises all the the "fake" Satans.