The left-leaning grouping has pledged to maintain the Baltic state's hefty defence spending program, while criticising the centre-right coalition government of Prime Minister Ingrida Simonyte over raising taxes to fund it.
Official government data showed the centre-left grouping leading with 52 seats in the 141-member assembly, after 99 per cent of the vote was counted.
Vilija Blinkeviciute is likely to lead a coalition government. (AP PHOTO)
The ruling Homeland Union Party was on track to take second place with 28 seats.
The Baltic country of 2.9 million people has a hybrid voting system in which half of parliament was elected by popular vote on October 13.
The remainder was decided on Sunday in district-based run-off votes between the top two candidates, a process that favours the larger parties.
SD leader Vilija Blinkeviciute told reporters she believed her party would have a parliamentary majority alongside its likely coalition partners: For Lithuania, plus The Farmers and Greens Union.
"The results of this election showed that the Lithuanian people, no matter where they live, in large cities, in small cities or villages, they want change."
She declined to confirm whether she would seek the job of prime minister: "We will discuss this within the party, we will weigh all pluses and minuses".
The For Lithuania party was on track to win 14 seats in the parliament and The Farmers and Greens Union was getting eight seats, provisional official data showed.
Simonyte's centre-right three-party coalition has seen its popularity eroded by inflation that topped 20 per cent two years ago, deteriorating public services and a widening rich-poor gap.
Domestic economic issues were in focus during the election campaign, with the SD vowing to tackle increased inequality by raising taxes on wealthier Lithuanians to help fund more spending on healthcare and social support.
But national security is also a major concern in Lithuania, which lies on the eastern flank of NATO and the European Union and shares a border with the Russian exclave of Kaliningrad and Belarus, a close Moscow ally.
Lithuania will spend about three per cent of GDP on its armed forces this year, according to NATO estimates, making it the military alliance's sixth-biggest spender.
Three-quarters of Lithuanians think Russia could attack their country in the near future, a Baltijos Tyrimai/ELTA opinion poll found in May, following its attack on Ukraine in 2022.
