The closures largely paralysed transportation.
US President Donald Trump said on Monday that if anything bad happened in Hong Kong it would be bad for the US-China trade talks.
On Friday, Lam had invoked emergency powers for the first time in more than 50 years to outlaw face masks.
Lam has faced widespread criticism over her decision to ban face masks - ubiquitous in Hong Kong since a deadly SARS outbreak in 2003 - and thousands of Hong Kongers flouted the prohibition during an unsanctioned mass march on Sunday.
She said seeking Chinese intervention was provided for under Hong Kong's constitution but that she can not reveal under what circumstances she would do so.
She also called on the business communities, property developers and the society to do their part to help those affected to tide over the tough times together.
Making the app available on Apple's Hong Kong site was "opening the door" to violent protesters in the former British colony, it said.
China is pressuring Apple to censor an app used by Hong Kong protesters.
China dismisses such accusations, saying foreign governments, including Britain and the United States, have fanned anti-China sentiment.
Professors talk probability, actions regarding Trump impeachment process
Joe Biden is a leading candidate for the 2020 Democratic presidential nomination. Trump has denied any wrongdoing, calling the phone call "perfect".
"But please allow me to reiterate that if we are so proud of Hong Kong being a city that upholds and safeguards the rule of law, one important component of the rule of law is the law-abiding population", Lam said.
"I still strongly feel that we should find the solutions ourselves", Lam said.
While admitting that there would be "some complications and misunderstandings" while enforcing the new legislation, Lam said her government would take necessary measure "to provide for some legitimate defenses and exemptions for certain categories of people".
The clashes allegedly happened after Hong Kong Indigenous, the so-called localist group that Leung belongs to, mobilized supporters to the area.
The financial hub has been gripped by four months of rallies, and last weekend saw much of the city grind to a halt as masked demonstrators took to the streets in defiance of a controversial ban on face coverings.
HKmap.live relies on numerous users to report and track the deployment of police officers, cordons and their assets so that protesters can plan and coordinate their tactics for hit-and-run, flash mob attacks at government offices and train stations, while greatly reducing the risk of being waylaid and nabbed. Sixteen people have been charged with violating the anti-mask law, according to the government and public broadcaster RTHK.
The piece goes on to condemn Apple for abandoning its "social responsibilites" and allowing the violence in Hong Kong to escalate.
Hong Kong's metro, which normally carries some 5 million people daily, was only partially operating on Tuesday.
Lam noted that a Chinese military intervention is in accordance to Hong Kong's constitution, known as the Basic Law, but said she "cannot reveal" the circumstances of when she would enforce such an intervention.