Activists occupied the Legislative Council (LegCo) building for hours after breaking away from a protest, the BBC reported.
The chief executive held a pre-dawn press conference after police had fired tear gas and evicted the intruders.
Lam called it a scene that "really saddens... and shocks a lot of people".
Flanked by Police Commissioner Lo Wai-chung, she said the actions of those who broke into LegCo were "something that we should seriously condemn, because nothing is more important than the rule of law in Hong Kong".
Peaceful demonstrations had been planned for Monday, the 22nd anniversary of Hong Kong's handover from British to Chinese rule.
The day is normally marked by an annual pro-democracy march - but this year's event followed weeks of unrest in the city over a controversial extradition law, under which critics fear political dissidents could be sent to mainland China.
Around midday, dozens of demonstrators broke off from the main protest and made their way to LegCo. They effectively besieged the building, as a large crowd of several hundred watched from a distance, before eventually smashing their way through the glass facade.
Inside, they defaced the emblem of Hong Kong in the central chamber, raised the old British colonial flag, spray-painted messages across the walls, and shattered furniture.
At about midnight outside the building, protesters clad in plastic helmets and brandishing umbrellas retreated from a baton charge by riot police, who quickly overcame their makeshift barriers.
Within an hour, the streets around the building were clear of everyone except the media and police.
( With inputs from IANS )