If any abilities trigger as you sacrifice permanents, those abilities won't be put onto the stack until after you've returned creature cards from your graveyard to the battlefield.

You sacrifice the artifacts, enchantments, and/or tokens as part of the resolution of Lich-Knights' Conquest. It isn't an additional cost. If Lich-Knights' Conquest is countered, you won't sacrifice anything.

You can choose to sacrifice zero permanents.

An artifact creature or enchantment creature sacrificed to Lich-Knights' Conquest may be one of the cards chosen to be returned.