He'll be a recurring character who first appears in 4x15. Fun fact, Jon Cryer played Lenny Luthor in Superman IV.
"We are enormous fans of Jon Cryer, and he was instantly our dream actor to play the iconic role of Lex Luthor. Jon is a super-talent, and the fact that he played Lenny Luthor in Superman IV brings an added layer of legacy to his casting. We’re beyond thrilled to welcome Jon to the Supergirl family," said executive producers Robert Rovner and Jessica Queller.