The man you are talking about is the man with the blowtorch to Martha whom batman murdered. And all the incriminating evidence Bruce gathered on Lex was illegally obtained which makes in inadmissible in court and subjects anyone who handled it to very serious Criminal charges.
Yes, there may be sand from the desert on lois' notebook. It's well known Lois was in the desert, it's natural there would be sand on her notebook, none of that proves anything. The prosecution has no murder weapon, they have no suspect, and they have no access to the crime scene, and they have no jurisdiction to get access to any of those things.
And the General states his knowledge of the situation was classified and there was nothing presented in the film to imply any of that was changing.
If the film featured a story arc for Lois where she legitimately and thoroughly investigates the conflict and gathers enough admissible and irrefutable evidence against Lex, yes that would of been an awesome character arc which would of been way better than her falling off things and drowning and playing Superman's constant damsel in distress.