When we interpret "nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb" do we naively say that someone found innocent of murder can never ever be charged of the crime of murder again?

Offence refers to the act itself not the name of the crime. I lied to you and I lied to another person, leading to a loss of money on both their parts. Shouldn't both individuals be able to seek recourse? If one loses his case, the other loses his case as well?

Even if this all works out legally, I am not sure I like the practical implications of it.