Jeffrey Epstein was many things: a sexual predator, a friend to the rich and powerful and, for many years, a lucrative customer of the nation’s largest bank.

Now the bank, JPMorgan Chase, faces a reckoning for its nearly 15-year relationship with the disgraced financier, one that could cost it a big payout in two civil lawsuits that claim the bank ignored warnings that he was trafficking teenage girls for sex because it was profiting from its relationship with him.

New disclosures resulting from the cases suggest that employees of the bank flagged Mr. Epstein’s activity as suspicious on a number of occasions, while other documents show Mr. Epstein’s familiarity with top executives at the bank, and his easy access to them, even after his 2008 guilty plea in Florida to soliciting prostitution from a teenage girl.

Filed late last year in federal court in Manhattan, the lawsuits — one brought by lawyers representing Mr. Epstein’s victims and the other by the government of the U.S. Virgin Islands — are proceeding on a fast track, with dozens of depositions taken of victims, Virgin Islands officials and people who worked for the bank and Mr. Epstein.