Russia had 5,000 to 5,500 troops at Lyman, but the number of encircled troops could be lower because of casualties, Cherevatyi said.
The Russian grouping in the area of Lyman is surrounded, the spokesman said on television.
The Russian Defence Ministry didn't respond immediately to a request for comment.
Russia's last operational update was on Friday evening. On Saturday, the ministry's Telegram channel published a series of congratulatory messages, including one from Putin, to mark an army holiday, Ground Forces Day.
Russian military bloggers said the loss of the town would be a serious setback and it was obvious that Moscow had taken the decision to abandon the city and withdraw its forces.
Neither side's battlefield assertions could be independently verified.
Russia has used Lyman as a logistics and transport hub for its operations in the north of the Donetsk region. Its fall would be Ukraine's biggest battlefield gain since a lightning counter-offensive in the northeastern Kharkiv region last month.
The Ukrainian military spokesperson said the capture of Lyman would allow Kyiv to advance into the Luhansk region, whose full capture Moscow announced at the beginning of July after weeks of slow, grinding advances.
He said it was an opportunity to go further to Kreminna and Sievierodonetsk and that it is psychologically very important.
The Donetsk and Luhansk regions together make up the Donbas region that has been a major focus for Russia since the beginning of Moscow's invasion on February 24 in what it called a special military operation to demilitarise its neighbour.
In Friday's ceremony, Putin declared the Donbas regions of Donetsk and Luhansk and the southern regions of Kherson and Zaporizhzhia to be Russian land, a swathe of territory equal to 18 per cent of Ukraine's total land area.