How to get this quest
You get this quest from Roland in the Knights Keep after completing Rampaging Golem.
Initial investigation
Speak to the Lumerian soldier west guarding the noble district of Verdeaux to access Laval's mansion. Once there, you'll get introduced to the main elements of the case.
You must collect evidence on the second floor before talking to the judge and proceed with the next part.
Furthermore, some optional actions can be taken before talking to the judge and help during the trial.
Once you are ready, talk to the judge to start the trial. You will have 4 lives (plus a lifeline if you blackmailed Marie). Any time you present evidence against a statement that doesn't show a flaw in the testimony, you will lose a life. If you lose all lives, the judge will take over and you will get a “bad” ending.
Pre-recess part
You will be given the option of trying to find a hole in François's initial testimony, or back down (7 Vice requirement). If you choose the former, move on to “Solving the case”. If you back down, move on to “Framing Lorraine”. The day will end when the judge calls a recess. Talk to François to continue the trial.
Solving the case
François will call a recess and try to convince you to frame Lorraine instead. If you choose to accept his offer, move on to “Framing Lorraine”, otherwise continue.
Framing Lorraine
You will get here either by backing down during François's first testimony, or accepting his offer after the first trial phase. Either way:
Continuing has a 10 Vice requirement. If you tampered with the formula, you will now be prompted to use that or stop (12 Vice requirement, this makes François give you 1000 G). Then you can use the Diary against her (14 Vice requirement) or stop. Finally is the choice to “Destroy Her!” (15 Vice requirement) or stop. If you went all the way with discrediting Lorraine, you will have the choice to make her Roland's slave (17 Vice requirement) or send her to prison.
Aftermath
If you completed the Vice path with tampered evidence and made Lorraine a slave, the reward will be 10,000 Gold (1500 base reward, 1000 + 500 from François, 7000 for slavery). Not tampering with the evidence will net you 9,000. Roland's popularity will also increase by 20.
If you lost all your lives on the Vice path, chose to stop before finishing, or didn't have enough Vice to continue, you'll get 1000 Gold plus a bonus based on how many vice choices you successfully made. For 4, the bonus is 2500; for 3, it's 1500; for 2, it's 750, and for 1, it's 250.
If you completed the pure path, Roland will lose 20 Popularity and he won't reward you. But Lorraine will stop you as you come out of his office and give you 1500 Gold.
If you lost all your lives on the pure path, you'll get a token reward of 150 Gold.
No matter the outcome, you'll receive 40 EXP.