Technically once again...Lapis original plan is to be a sacrifice (Scapegoat) to boost the prince's reputation and have Diana appear as a hero for the commoners so Commoners and Nobles will never long fight/civil war risk while killing off the crazy radical commoners...I don't consider Lapis' plan to be that pointless...but yes her plan is somewhat stupid and suicidal very much yes [Could have pin the blame on some corrupted noble]...If Lapis or some other smart character was in IRL...They would be smarter than 60% of the world population lol.
Lapis' original plan didn't count with her sacrifice nor was meant to boost the Prince and Diana's reputation, it was straight up just eliminating all commoners, she died because she was the villain of the story and that was how the story was written.
Honestly sure Lapis plan was solely focus on killing all the commoners involved in her Adopted sister's death but that did not mean she not willing to die at the end after she got her revenge. She is a smart girl that fooled the Gamers/Fan-based who played the otome game into thinking she is a totally nice person (Chapter 1- Stealing magic jewel for magic booster).
She could easily just adjust her plans to let herself be killed to boost the (Her Fiancee) Prince's reputation and Diana's reputation. Kill off all the commoners from the Anti-Noble fraction that she saw responsible for her little sis' death [Any innocent bystanders are acceptable casualties though to her lol... (Lapis' trauma from chapter 2 and other chapters)] then Lapis can be satisfied dying either way...because if Lapis want to survive she could have flee to another country and be a thorn to the Prince and Diana easily with her influence and power.
Chapter 8 (Lapis teaches prince that he is the player and not the chess-up...Queen piece dropped as she talk about the bigger picture, Lapis tells prince there is no way to preserve all the pieces and even refers that she is a chess piece too...).
Since she probably achieved her goal then she was ready to set things up to so her death is at least beneficial to the Prince and the future of the kingdom...she would have sacrificed her family, the prince and Diana if she didn't achieved her goal of killing all the [Anti-noble member (Low rank nobles are helping them due to greed for more power which can cause civil war)] but since she got her goal finished in the original timeline then she doesn't have to go that far for her [REVENGE].
I won't deny Lapis want to kill all the commoner [Mainly from the Anti-noble fraction (Any innocent people dying are probably acceptable to her though since she will rationalized it as the Bigger picture idea thing)] but she cares about the prince, Diana and her family to a small extent...not enough to not kill them for her plans for [REVENGE] but enough to not cause trouble for them in the future...The MC here on the other hand...Lapis cannot sacrifice the MC for [REVENGE] due to being to involved/care about MC too much. Lapis tried her best to keep herself emotional distance while making sure MC's life will be comfortable and somewhat happy but failed lol
MC and the gamers seem to not know much about Lapis' backstory (MC does not know about the little sister except Lapis throw away line about having a commoner sister) and the reasons why she want [REVENGE].
You can call my idea and analysis of Lapis' character stupid and wrong, saying her wanting to kill the commoners is not deep and that is just the way she is written in the game but eh whatever, Agree to disagree XD