They don’t know how it happened. She just got snatched off the street on the way back from a party with her friends, and JARVIS alerted them.
Of course, Tony would go out of his mind. His princess has been taken. She should have been at home with them, drinking hot chocolate and watching crappy rom-coms. He almost makes himself sick with worry.
Steve, of course, goes all Commander Rogers on the situation. He has JARVIS go through all the CCTV footage in the city to try and find her, but whoever’s taken her is clever, because they’ve wiped all the tapes across the city for that night. She could be anywhere.
It’s twelve hours before they receive the ransom tape. Lily already looks beaten to hell and terrified out of her mind, and Tony has to excuse himself to physically vomit.
They meet the HYDRA agents on the bank next to the Brooklyn bridge, and are planning to screw them over and give them false information in a briefcase, but they open the briefcase before Steve and Tony can get Lily safely away, and Tony ends up getting shot in the back protecting her. The other Avengers and what’s left of SHIELD arrive to ambush the HYDRA agents, and Tony and Lily are taken to hospital.
Everyone makes a full recovery, and Lily sleeps in her dads’ bed for a full month afterwards, even though she’s eighteen.