Both have a very unusual female lead that is trying to solve cases.In both dramas they have a young male that is their assistent and has a hidden identity. Only difference is that "Cheat on me if you can" has also a side story of the husband, which is not found in Goritekini.

Both dramas deal around two older women that are both quirky and unusual. Both are becoming sort of detectives after they have taken a hit to their careers. Both are working with a young man, who is their assistent but actually watches out for them. Both are very fun and at the same time serious dramas.

Both dramas are related to the Light On series of Iqiyi. In Both dramas Qin Hao plays a police officer that gets involved in a case that threatens his career and causes him to be degraded. In both dramas he is getting a 2nd chance to clean up his name and also find the culprit of the case.
Both are well done crime dramas.

Both works are based off of novels written by Kanae Minato.
Both stories feature storylines where women undercover the real connection behind a case.

Both dramas are very similar in the regards to the story. Both female leads end up in an alternative world, where they meet people, who they know in the real world, but now with different identities and lives. Both female leads suffer from a sort of "amnesia". Both investigate a case, that is the reason for their situation. Both dramas revolve around a romantic interest, that is connected to them in the real world.
The biggest difference is that Shards of Her is a more traumatic drama, whereas Lost Romance has a more lighter take on it.

characters end up in the past, reliving traumatic experiences. Both dramas revolve around a female lead that investigates the case with the help of the guy, that they are/were in a relationship with.

Both dramas evolve around a group of police people that end up being confronted with criminals. Both have to question justice and end up in situations that makes them question their own morals. Both dramas have as a side plot a romance story and both have quite a similar ending.

Both drama are about a woman who are is unhappy in her marriages, who wishes for a family but failed to have one, who has friends that are rich, influential and have the life that she wishes for. Both women end up in a situation where they acquire a lot of money and are tempted to use that money for themselves. Both set of a chain of actions because of that money.

Both dramas are following a selected amount of detectives chase a suspect over many years. We see how the detectives but also the suspect and witnesses of the crimes change and evolve over time. Both dramas give off a very similar vibe. If you liked one you, might very much enjoy the other one as well.

Both dramas have cases where the killer is playing mind games on his victims. In both dramas characters end up questioning their own morality and have to make decisions that turn them from good to bad.

Both dramas revolve around a culprit that will go to unusual means to open an old case again. Both dramas have a great plot, amazing cinematography and great cast.

Similar story. An old case is reinvestigated.
People will go to unusual means in order to investigate the truth behind an old case. If you enjoyed Trinity of Shadow you will surely enjoy The Post-Truth World.