Lancer always dying is a joke in carnival phantasm, the reason why he dies is or who kills him is of little importance. For example, in one of the first episodes of carnival phantasm when the cat characters are talking with the TV on we hear about a man in blue thighs being killed in a car accident. It is of course Lancer, and he just died for no reason whatsoever.
For your case though not a lot of people could have killed him because we can see black keys in his body, the weapon of the church. It means a priest must have killed him.
The only person I could see doing that would be Kotomine, because we also see him asking Grail-kun to do something because Lancer is completely useless, and Grail-kun gives him the "Servant Strengthening Tool" (The kitchen knife in the picture).