Unlike Stockholm syndrome, where hostages develop sympathy for their abductor, Lima syndrome is the result of the abductor / kidnapper sympathizing with his hostages.
Occurred in the Japanese Embassy hostage crisis of 1996, when members of a militant movement took hostage hundreds of people attending a party in the official residence of Japan's ambassador to Peru. Within a few days, they set free most of the hostages, including the most valuable ones.
In The World is Not Enough, James Bond thinks Electra King (Sophie Marceau) has Stockholm Syndrome for her kidnapper / lover Renard (Robert Carlyle). However, it turns out that Renard really had Lima Syndrome, and loved Electra deeply.