Warning: The following contains SPOILERS for Superman and Lois season 2, episode 4, "The Inverse Method."
The Superman and Lois retcon of Lucy Lane's background from Supergirl is a mistake, which weakened one of the Arrowverse's most interesting characters. The Lucy Lane of Supergirl was an honest, iron-willed military lawyer with a high-level of self-confidence. This stood in marked contrast to her recent appearance in Superman and Lois, which painted her as weak-willed and manipulative.
Played by Jenna Dewan, Lucy Lane entered Supergirl season 1 as a romantic rival to Kara Danvers for James Olsen's affections. She quickly came to be an antagonist to Supergirl as well, after she reenlisted in the US Army JAG Corps, where she held the rank of Major, and served as a legal adviser to her father, General Sam Lane, before taking over the DEO. Despite being skeptical of alien heroes, Lucy did not share her father's fear of them and came to be an advocate for Supergirl and the Martian Manhunter J'onn J'onzz by the end of Supergirl season 1. She was also remarkably reasonable regarding her relationship with James Olsen, which she ended after realizing he was clearly much more comfortable with Kara than with her. Lucy Lane disappeared from the cast of Supergirl after season 1, but she was on good terms with the Super Friends during her last appearance on the show.
Jenna Dewan played a dramatically different version of Lucy Lane in the Superman and Lois season 2 episode "The Inverse Method." The episode opened with a flashback to five years earlier, where Lucy Lane was packing up her belongings and preparing to leave Lois and Clark's home in Metropolis, where she had been staying after losing her job and her fiancée. This immediately conflicted with the Arrowverse timeline established by Supergirl, where James and Lucy were never engaged and Lucy had unlimited career prospects given her military service and her experience as a lawyer who graduated from Harvard with JD and MBA degrees. More importantly, this version of Lucy Lane seemed to lack the confidence and strong moral fiber that defined the character on Supergirl and made her an interesting antagonist, given that she was just as moral as Kara Zor-El.
While Jenna Dewan delivered a convincing performance as the new Lucy Lane, the character seemed to be an easily manipulated dupe with no purpose beyond being a victim for Lois to rescue. Her behavior in the present further established this new Lucy Lane as a treacherous person, who helped manipulate Lois as part of a scheme set up by self-help guru Ally Allston, whom Lois had exposed as a dangerous cult leader years earlier.
This is not the first time that Superman and Lois has made a major change to the history or personality of a character once prominently featured on Supergirl. The series recast Dylan Walsh in the role of General Sam Lane, presenting a new version of the character who was fully aware of his son-in-law's secret identity and less xenophobic than the one played by Glenn Morshower in Supergirl season 1. The show also reworked corrupt billionaire Morgan Edge, who was played by Adrian Pasdar in Supergirl season 3. Recast with Adam Rayner in Superman and Lois season 1, Edge was also given a new backstory which established him as Superman's half-brother, Tal-Rho. However, while these changes resulted in richer, more nuanced characters, the same cannot be said of the new Lucy Lane featured in Superman and Lois.