"The only thing we have to do is to go against violence, and rebuild the city," said Lam.
According to the airport's website, a handful of flights departed after midnight.
Demonstrations initially kicked off at the airport on Friday, with a small number continuing protesting over the weekend. Monday's mass gathering at the airport was sparked by widespread allegations of police violence during protests on Sunday.
At a sometimes rowdy press conference on Tuesday morning, Lam said the city had experienced "damage" caused by the "illegal activities" of protesters who "did not have the law in mind."
"Riot activities (have) pushed Hong Kong to the brink of no return," said Lam. She said protesters had attacked "police officers with malice intention" and insisted "police are an important defense of Hong Kong."
Lam's comments come as protest organizers called on supporters to return to the airport Tuesday, for what would be the fifth consecutive day of demonstrations at the aviation hub.
"We stayed here overnight because we want to show people it's safe in the airport," said one 23-year-old protester, Tuesday, one of around 30 demonstrators who had stayed in the arrivals hall overnight.
"We are expecting more people to join in in the afternoon and with enough people, we hope to paralyze the airport once again like we did yesterday," added the protester, who would only give his first name, Pang.
Confused tourists were left unsure of what was happening as shops, restaurants and check-in counters closed. Trains and buses heading into the city were packed with people, and the one available information desk was helmed by frazzled looking staff.
Some travelers were pragmatic about the delays. Hayden Smyth, a tourist from Australia, said it was a "bit of a different welcome than I'm used to."
But others were frustrated by the cancellations. "We love Hong Kong but it does change our whole perspective," said Australian Kim Macaranas, whose flight was canceled Monday. "I understand the protests but this is not helping tourism."
On Tuesday morning, disagreements broke out at the airport. Two men -- one of whom was wearing a cap emblazoned with a Chinese flag -- were seen arguing with protesters in the arrivals hall, before being ushered away by security as protesters cheered. Another passenger -- who appeared to be from mainland China -- told protesters that they were causing inconvenience for others.
Hong Kong's protest movement kicked off in earnest in June, sparked by a bill that would allow extradition to China.
Since then, the protests have expanded into something bigger, with protesters now demanding greater democracy and an inquiry into alleged police brutality. The protest movement -- that on Sunday passed its 10th straight weekend of demonstrations -- has seen protesters and police clash numerous times, with police firing multiple rounds of tear gas.
CNN's Jadyn Shum, Angus Watson, Ben Westcott, James Griffiths, Jessie Yeung and Helen Regan contributed to this story.