The Truth (2021)

Both are crime-solving and investigation drama
both FLs and MLs have cute chemistry but no romance in both dramas
both leads are cohabitating

Both focus on investigating to find evidence to bring justice to crimes made. In Hello Procurator, the ML investigates the death of his parents, while in Truth the FL investigates the mystery of her father's death.

-Both dramas involve the public prosecutors office. The importance of their role is emphasized when it comes to uncovering the truth behind trial cases.
-In 'Black Lighthouse', intense confrontations between prosecutors and defense lawyers in the city courthouse takes place during trials where court evidence and the most minute details determine a persons acquittal or conviction.