task The Mystery of the Cabbot House (Fallout 4)

If you choose to kill Lorenzo, then he will be dead. If released, then he will be free.

in the sense of what the consequences will be next and what reward they will give

Administration Builder

for the murder of Lorenzo you will be called "the killer of Lorenzo", for the release of "the liberator of Lorenzo"

Builder Administration
and the pistol Lorenzo that shoots the gamma of ammunition will not be?

Quest spoiler!
Spoilers for murder will be given a cannon to Lorenzo, for released they will be given a Zeta cannon and a bottle of blood. The gun from the first option is better, as for me. But if you save, you will meet Lorenzo again and he will give a small investigation task.
But there is another option: to save, and then kill. Then they will give a gun from the first option and blood from the second.

Administration Builder
but I killed Lorenzo and Jack says come back to the cabot house in a week

david2222
That's right, time can be stretched by sleeping. But he will give a gun, only if in dialogues with him he was not rude and rude.