Hi!

How exactly Underrealm Lich works in 2HG? Does player controlling it knows which card their partner draws for turn before picking which card to put into their hand?
Do these actions happen simultaneously or players can choose an order?

Thanks in advance

In 2HG if multiple players on the same team need to draw cards at the same time each of those players performs their draws in whatever order the team likes. This means that the team can decide to have the player who doesn't control Underrealm Lich draw their card for the turn first, and then the Lich player afterwards. If they do so, the Lich player will therefore know what card their teammate drew when making their decision of what to keep.