The Suit of Sorrows was created in 1190 during the Crusades, by a splinter sect of the Knights Templar known as the Order of Purity. It was crafted and forged from the melted blades and breastplates of several soldiers of the Order who had fallen in battle as well as some magical metal old texts refer to as "Starmetal". It was designed to be worn only by their champion, Sir Geoffrey De Cantonna.
Sir Geoffrey De Cantonna was a Knight in the Order of Purity who, while a great warrior, was far from pure of heart. He wore the suit for several lifetimes, his life extended by the suit, but the dark secret of the suit slowly made itself manifest. The suit was secretly powered by a demonic soul. That's why it could only be worn by the most pure of heart and Geoffrey wasn't up to the task. The rites which had kept the demon in check for ages had been defeated and the demon drove Sir Geoffrey insane, compelling him to slaughter hundreds, perhaps thousands of innocents until he was stopped by a group of heroes called the Demon Knights.
The armor was intended to be returned to the Order of Purity but it was stolen by Al Jabr. Al Jabr and the demon inside the armor more or less became one and the fusion of identities granted him power, which he used to have revenge on raiders who killed love of his life. In the aftermath Al Jabr took the armor off and proclaimed himself the demon's master. 
The Suit of Sorrows was owned by Ra's and used by the Safinat Dakhma for centuries. In the past it was worn by Bruce Wayne, it was given to him as a wedding gift by Talia al Ghul. He left it behind when he escaped the League.
When the League planned the Cataclysm, they gave Jean-Paul Valley the Suit and the name Azrael, the Fourth Horseman, meant to kill and replace Batman. When Bane, the Second Horseman, got carried away and instead of breaking the Bat, he tried to kill him, Dick Grayson took on the mantle of Batman. Feeling lost and without purpose, Azrael became a vigilante in Gotham until Dick approached him to lead the newly formed Sons of Batman.
Jean-Paul put the suit away, and for a while he lead the Sons as a vigilante group; but after a while (probably under the influence of Joseph Blackfire), the Sons became more criminal than vigilantes. Eventually, Jean-Paul decided to partner up with Michael Lane, a former member of the Sons, and now detective of the GCPD, to take out the Sons competitors in illegal activities. Jean-Paul gave Lane the Suit of Sorrows and he became the second Azrael.
Lane was later apprehended by the Bat Family; but instead of taking him to the authorities, Dick, who was again taking the Batman identity (while Bruce was missing), decided to take him to the secret prison in the Batcave 4. Dick planned to dress Luke Fox as Azrael to trick the Sons of Batman and take them down.
But before they could put their plan in place, they were approached by Talia al Ghul, who knew the whereabouts of Bruce. Talia and Dick made a deal, than probably included Dick handing over the Suit of Sorrows back to Talia.
Months later, Shelly Gaynor showed up in Gotham and stater calling herself Heretic. She was defeated by the Seven Soldiers of Victory and her armor taken away. When Agent Parker opened a vault where it was stored, Shelly woke up and stole the armor.
Trivia and Notes
- It's also called the Raiment of Sorrows.
- The Lamentation Blades (also known as the Laminas Pesar) were once part of the armor, but were forcibly removed from the armor by Diana. The blades were taken back to Themyscira by the exile on accident. Themysciran artificers repaired the blades and stabilized their magic. These blades are currently used by Scandal Savage. These gauntlet mounted blades have the ability to slide out through mental trigger of their master (even if not currently wearing them). The blades steal a portion of the soul of anyone they cut, leaving a curse of sorrow in their place. Weak-willed persons who survive a cut from the Laminas Pesar often end their lives weeks later, seeking an end to their misery.