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Hong Kong's government is duty bound to safeguard its own situation under the principle of "one country, two systems" -- by which the city retains certain autonomy and freedoms -- but Lam told CNN that the bookseller case "has to be dealt with in accordance with the mainland's system."
All five were associated with publisher Mighty Current, which has put out books critical of Chinese President Xi Jinping and other leaders.
He later fled during a one-day release to Hong Kong in which he was meant to gather evidence against himself. But instead he went public with his story.
Speaking out
The UK is a signatory to the Sino-British Joint Declaration under which the former British colony of Hong Kong was guaranteed certain protections and basic human rights.
"China is more and more regarding Hong Kong as part of China politically, even though the Sino-British Joint Declaration is supposed to protect against precisely this," Angela Gui told CNN.
"What happened to my father and his colleagues shows really blatantly how China ignores the treaty."
A spokeswoman for the Foreign Office told CNN the UK "takes our longstanding commitment under the Sino-British Joint Declaration very seriously. Hong Kong's success relies on the rights and freedoms protected by that international treaty, including the rule of law and an independent judiciary."
Angela Gui said that Hong Kong's leaders have also not done enough, and she was critical of Lam for referring "to the rule of law and 'one country, two systems' to excuse politically motivated kidnappings."
"The kidnappings of my father and his colleagues have everything to do with 'one country, two systems': They are a painfully obvious breach of it," she said. "As this has implications for the security of all Hong Kongers, one would have thought that the chief executive would be more concerned."
Carrie Lam said that while she "sympathizes" with Angela Gui's situation "at the end of the day we must respect the rule of law in respective jurisdictions."
Handover concerns
As Hong Kong prepares to mark 20 years of Chinese rule next month, the booksellers case looms large, Amnesty International researcher Patrick Poon said.
"People in Hong Kong, especially those working on sensitive issues, are still worried about their safety," he said. "Nobody can guarantee that something like Lee Bo's case won't happen again."
Artist and activist Kacey Wong said the booksellers case was a "game changer," leaving him and many others feeling like "anything can happen."