The capture came just a day after Putin proclaimed the annexation of four Ukrainian regions - including Donetsk, where Lyman is located - and placed them under Russia's nuclear umbrella, at a ceremony that was condemned by Kyiv and the West as an illegitimate farce.
The Ukrainian soldiers made the claim in a video that was recorded outside the town council building in the centre of Lyman and posted on social media by Kyrylo Tymoshenko, deputy head of President Volodymyr Zelenskiy's office.
"Dear Ukrainians - today the armed forces of Ukraine ... liberated and took control of the settlement of Lyman, Donetsk region," one of the soldiers says. At the end of the video, a group of Ukrainian soldiers throw Russian flags down from the building's roof and raise a Ukrainian flag in their place.
Hours earlier Russia's defence ministry had announced it was pulling troops out of the area "in connection with the creation of a threat of encirclement".
Russia had used Lyman as a logistics and transport hub for its operations in the north of the Donetsk region. Its capture is Ukraine's biggest battlefield gain since a lightning counteroffensive in the northeastern Kharkiv region last month.
Zelenskiy promised more quick successes in the Donbas, which covers the Donetsk and Luhansk regions that are largely under Russian control.
"Over the past week, the number of Ukrainian flags in Donbas has increased. There will be even more a week's time," he said in an evening video address.
He also indicated Ukrainian troops had taken the village of Torske, on the main road out of Lyman to the east.
The recent successes have infuriated Putin allies such as Ramzan Kadyrov, the leader of Russia's southern Chechnya region, who said he felt compelled to speak out.
"In my personal opinion, more drastic measures should be taken, right up to the declaration of martial law in the border areas and the use of low-yield nuclear weapons," Kadyrov wrote on Telegram before Zelenskiy spoke.
Other top officials, including former president Dmitry Medvedev, have suggested Russia might need to resort to nuclear weapons, but Kadyrov's call was the most urgent and explicit.
Putin said last week he was not bluffing when he said he was prepared to defend Russia's "territorial integrity" with all available means, and on Friday made clear this extended to the new regions claimed by Moscow.
Washington says it would respond decisively to any use of nuclear weapons.
