Lam's comments, in a statement released late on Wednesday, came after Chinese President Xi Jinping told Hong Kong's leaders their "overriding mission" was to stabilize and control the coronavirus in the global financial hub.
"With the utmost concern and staunch support of President Xi Jinping... all in society must now join hands in riding out the fifth wave of the epidemic, displaying the Hong Kong spirit in full," she said.
"I once again appeal to the people of Hong Kong to remain confident and support the government's anti-epidemic measures."
In a move to free up beds for isolation, Lam said she had spoken with local hotel owners on Wednesday to identify up to 10,000 hotel rooms for patients. Security chief Chris Tang would oversee the operation of participating hotels, she said.
Hong Kong has adopted the same 'dynamic zero' coronavirus strategy, employed by mainland China to suppress all outbreaks.
But the scale and speed of the highly contagious Omicron variant of the virus has left authorities scrambling. Hospitals are operating at maximum or over capacity with some patients treated in makeshift open air spaces outside medical centers in chilly and rainy weather.
Authorities said they could no longer keep up their testing and isolation mandates, resulting in a backlog that could not keep pace with the daily infection numbers.
China has said it would help Hong Kong bolster its testing, treatment and quarantine capacity, and secure resources from rapid antigen kits and protective gear to fresh vegetables.
Hong Kong has recorded around 30,000 infections since the start of the pandemic, and around 230 deaths, far fewer than other similar sized major cities.
Health authorities reported a record 4,285 confirmed new infections on Wednesday, and another 7,000 preliminary positive cases, a massive surge from around 100 daily cases at the start of February but still lower than in other similar sized major cities.
However, medical experts have warned daily cases could surge to 28,000 by the end of March amid worries about high levels of vaccine hesitancy among the elderly.