I thought this was a good summary of what we know about the last 48 in Lyman.
Ukraine update: As Ukrainian forces enter Lyman, hundreds of Russians may still be trapped inside
Here's an excerpt. The whole thing is worth reading.
It now seems possible to put together something of a picture of what happened in the last 48 hours from a mixture of sources. As the perimeter around Lyman tightened, Russian forces that had been in Yampil and Drobysheve first went into Lyman, then began withdrawing along the road to the east. There was an effort to remove heavy equipment, including the artillery that had backed the Russian position in Lyman over the last two weeks. Within hours, many of the Russian infantry began to follow, but all of this made for slow progress down relatively small roads.
Throughout Thursday and Friday, those Russian forces issued many requests for reinforcement or rescue, and were sent assurances it was on the way. There are even messages from the Bakhmut area complaining that Wagner forces left the front lines there to go to Lyman. However, if any of those forces ever made it to Lyman, it doesn’t get mentioned. Most likely, any relief force that was sent never got closer than the intersection between Torske and Zarichne, where they may have helped to temporarily hold Ukrainian forces back from the road.
As the escaping forces ran a gauntlet of Ukrainian artillery, anti-tank weapons, and heavy machine gun fire, they took significant losses. Damaged armor clogged the route. They were also slowed because the road leading into Lyman had been mined or damaged at several locations.
At some point, Russian troops (some reports suggest members of BARS-13) blew up the bridge across the Zherebets River north of Torske to prevent Ukrainian pursuit. This may have helped some escape to the east, but it also trapped the forces following them, leading to an intense fight near Zarichne as those forces attempted to find a way out.