Havengul Lich

[Antirayman]

Can you cast a creature card from a graveyard  with {Havengul Lich} then sacrifice it and recast it with out paying an additional {1}?

[Paraluke]

You need to pay the cost every time you use it, regardless of whether you are targeting the same card.

Not sure if that is what you mean.

[Spikepit]

Nope. If you want to use his ability, you have to pay {1} each time. 

[Kaleo42]

The creature becomes a new object as it changes zones. Even though you targeted that card once with the ability the game says you already cast the creature you targeted and now their happens to be a identical looking creature in the graveyard that has not been targeted yet.