Complex sentence: Snape, who had not realized until too late that the prophecy was referring to Lily and her family, asked Voldemort to spare Lily, and in terror for her life, also approached Dumbledore, admitted his actions, and begged him to protect the Potters.
Split into simpler sentences: Snape, who had not realized until too late that the prophecy was referring to Lily and her family, asked Voldemort to spare Lily. Still in terror for her life, he also approached Dumbledore, admitted his actions, and begged him to protect the Potters.