"We're staying in an open session until further notice," lawmaker Najat Saliba told Reuters by telephone on Friday, a day after the sit-in began.
She is one of 13 independents elected last year in an election that otherwise left the 128-seat parliament in the grip of long-dominant sectarian factions that will ultimately determine the fate of the presidency.
In a video filmed in darkness on Thursday evening, she said, "We are here to implement the constitution ... remaining in the parliament until we elect a president."
Lebanon has had neither a president nor a fully empowered cabinet since Michel Aoun's term ended in October, further complicating the path out of a financial meltdown left to fester by the ruling elite since 2019.
The currency collapsed on Thursday to a new record low of 50,000 Lebanese pounds to the dollar, marking a devaluation of more than 95 percent since 2019 that has impoverished the nation.
Lebanon's divisive politics has resulted in the presidency - reserved for a Maronite Christian - being left vacant numerous times.
The thresholds needed to secure a quorum and victory in the parliamentary vote mean no single faction or alliance has enough seats to impose their choice.
Aoun became head of state in 2016 with the support of his powerful Shi'ite ally Hezbollah in a deal that also brought Sunni Muslim politician Saad al-Hariri back as prime minister.
International rivalries, which have long played out in Lebanon's domestic crises, have often complicated the process.
Hezbollah and its allies have close ties to Shi'ite-led Iran and Syria, while their opponents in the Christian and Sunni communities look to the West and Sunni-led Gulf Arab states.
The heavily armed Hezbollah, Lebanon's most powerful group, has said the new president should be someone with broad support.
Anti-Hezbollah lawmaker Michel Mouawad has won the most votes in 11 unsuccessful presidential election sessions so far, but not enough to win.
The World Bank has accused the ruling elite of orchestrating the depression due to its exploitative grip on resources. The government has failed to carry out reforms needed to secure an IMF deal and unlock international support.