I think risci and I have offered up different win cons.
I see Han winning through a combination of observe, danmaku, and possibly his shackles. He has both magical and nonmagical ones. His danmaku should be straight up superior to Lich's, and his barrier and teleportation provide hard counters to anything that wouldn't get through, whereas Lich doesn't have this luxury, though Lich does have regen.
This means Han would likely have to use something like his magical shackles of binding, and essentially just keep him in those shackles. The Lich will be bound up and essentially defeated, unable to do anything.
Also, if Han opts to use Gnome, he could essentially trap the Lich in a hole the size of about half a city block.
Han could also potentially just outlast the Lich. Han's mana is always regenerating, and he has a variety of potions he can use for both his mana and his HP to continue the fight in the off event that those aren't enough.
His golems provide him with the win condition of stuffing the Lich into them. And, unless the Lich's summons are of his AP, Han's golems would go through them. It helps that Han can literally double their stats once a day.
Lastly, the Lich might fall victim to a self BFR in Han BFRs them both to an ID barrier, and Kaliber forces the Lich back, but Han avoids it with either flight, or teleportation.
Han's observe skill and intelligence, I would argue, are what really bring these win conditions together. As he'll have some knowledge of what to do, and always adapts his plans during the fight.