An antimagic field spell makes magical weapons into normal weapons for purposes of attack. Magical spells also lose their effects.
A lich is listed as having damage immunities to: Poison, Bludgeoning, Piercing and Slashing From Nonmagical Attacks. Liches also have condition immunities to: Charmed, Exhaustion, Frightened, Paralyzed, and Poisoned.
The only effects that penetrate an antimagic field are artifacts and effects from deities. Given the immunities of a lich, this seems to leave only fire and acid as a way to damage liches apart from artifacts and deities.
However, Jeremy Crawford previously wrote, "Antimagic field has no effect on a creature's immunities, unless those immunities are sustained by magic."
Are a lich's immunities "sustained by magic" as described by Crawford and go away in an antimagic field? More generally, apart from artifacts, deities, and fire, what can damage a lich in an antimagic field?