Assassin is Kiritsugu
Isn't it obvious?
Luvia will kill Assassin!Kiritsugu
Her contract was to kill the Magus Killer and she'll fulfill it by killing the original one and not Shirou. After all no one knows Shirou Emiya is the Magus Killer and no one would put a contract for a dead man so the contract was simply "to kill the Magus Killer".
Assassin!Kiritsugu will trick Witch!Caster into using up all her Command Seals
She's already had to use one just to get him to listen to her commands at all. Add one more to make him willing to fight his son, and a third to make him willing to fight his daughter, and suddenly Caster will find herself facing a very unhappy Magus Killer.
- Caster wasted the second one to get control of Rider. Now Caster has Three servants that want to kill her and only one command seal. She is not happy to say the least...