Since Lupin Part 2 will pick up immediately where its first part left off, its plot is expected to resolve some of the tension built up over the course of the series’ first five episodes. At the end of Part 1, a henchman working for Hubert Pellegrini kidnaps Assane and Claire’s son Raoul. As of the fifth episode’s conclusion, Raoul remains missing. Lupin is sometimes dark in tone but never hopeless, so Raoul is likely to make it back home at some point during Part 2.
Central to the tension between Assane and Claire is the fact that Claire is unaware of the extent of Assane’s secret life. That includes both his endeavors as a gentleman thief and an affair revealed in episode 5 between him and Hubert Pellegrini’s daughter Juliette. That issue is likely to be resolved in Part 2, whether through a reconciliation between Assane and Claire or their falling out.
Finally, Detective Youssef, as the story currently stands, is the only investigator suspicious of Assane’s role as a gentleman thief. How that knowledge might hinder Assane’s quest for revenge is likely to impact the story of Part 2.