The circumstances of unlocking the case: This case counts as a part of the games storyline mode and you receive it after your visit on the Penguin's ship ends. The mission in question is Solve the crime scene inside Lacey Towers.
After you gain access to the Lacey Towers go to the apartment that serves as Sionis' Safehouse, i.e. the crime scene which requires a very detailed scrutiny. Start by switching on the evidence scanner and scan the victim deemed to be the Black Mask (you need to press and hold down the key/button that the game prompts you to) to analyze the left hand fingertips.
Turn around and approach the chandelier to scan the woman hung here, thus learning her personals.
Another area that can be scanned is the floor near the chandelier with traces on it. Performing a scan here will allow you to determine the how the fire spread all around the apartment. Return to Black Mask's corpse. Scanning it once again will start another reconstruction, this time concerning the circumstances of the man's murder.
Approach the woman hanging down from the chandelier again and scan the corpse again. Also in this case, you will need to determine the fired bullet's trajectory. turn around and locate a new trace to the right of Black Mask's corpse. It is going to be fingerprints that can be subject to examination. Remain in this area and locate the shoe polish smears and scan them.
Take a look around the site for possible DNA on the floor, connected this time with the destroyed table. After you see another reconstruction, start holding down the keys/triggers for adjusting the reconstruction. Follow the red line, which will take you to the balcony door. You will find here a fragment of clothing, which you of course need to scan.
Go now towards the apartment's exit but, after you take the stairs, turn right and examine the counter on the right. Press, and hold down the appropriate key/button after you target the DNA trace shown in the above screenshot, thanks to which you will see another reconstruction.
Finally, find the cell phone lying on the floor. Examining it will allow you to read an important message. Watch the final version of events and listen to the conversation with Alfred.