In a three-minute video titled "Treasure Hong Kong... our home", Lam took stock of 2019, a year which, according to her, has "caused sadness, anxiety, disappointment and even rage", reports Efe news.
"I will listen humbly to find a way out so we can begin together," the leader said in the video posted on her Facebook page.
Lam expressed hope for reconciliation in 2020 and said Hong Kong people have "resolved many difficulties before."
However, some residents on Tuesday were back on the streets mobilizing meetings throughout the day and urging people to not forget what had happened in 2019 and continue protesting in 2020.
Hong Kong Police has deployed 6,000 officers to contain protesters during New Year celebrations, local media outlets reported.
Thousands are expected to gather Wednesday, New Year's Day, for a march called by the Civil Human Rights Front, a group that has mobilized more than 1 million pro-democracy protesters on earlier occasions.
Police have not authorized the march and warned in a video posted on its website that protesters would "not get public support" if they used violence and officers would be forced to arrest them.
Demonstrations in Hong Kong began in June following a controversial extradition bill, already withdrawn by the government, but have mutated into a movement seeking to improve Hong Kong's democratic mechanisms and safeguard the region's partial autonomy from Beijing.
Some demonstrators have opted for more radical tactics than peaceful civil disobedience and violent clashes with the police have been frequent.
Months of protests have plunged Hong Kong's economy into recession for the first time in a decade, having contracted by 2.9 per cent in the third quarter, due to falling imports and exports, retail sales and declining tourism.
( With inputs from IANS )