Joseph Lychkoff is a Ukranian immigrant, rampant gambler, and the abusive father of his daughters Elsa and Katrina. Joseph tortured his daughters to be scholarly successes, largely to pay off his gambling debts. Elsa was more a success than Katrina, who was disowned by Joseph and took care of herself to maintain her life and person.
Joseph was a suspect when Elsa was found dead in the Hudson River in New York. Ruling out she was sold in a sex trafficking ring, one trafficker, Alik, knew Elsa from her publicity. When Katrina arrived after hearing Elsa was dead, she brought SVU down to the basement where she was tortured, which cast suspicion on Joseph.
Joseph was arrested and interrogated, denying being Elsa's killer and trying to rationalize his own crimes. When he was screamed at to confess in interrogation, he voiced his apologies to Elsa before slamming his head repeatedly into the wall, fracturing his skull. He was immediately hospitalized, and later cleared of Elsa's murder when his alibi checked out, showing security footage of him at another casino. (SVU: "Hothouse")