Warning: The following contains SPOILERS for Superman and Lois season 2, episode 2, "The Ties That Bind."
The link between Supergirl and Superman and Lois is close to dead following new information regarding the Earth-Prime Lucy Lane. Despite being a Supergirl spinoff, Superman and Lois season 1 made no references to the series that inspired it. Indeed, apart from a cameo by Arrow's John Diggle, Superman and Lois has largely stood apart from the larger Arrowverse. While it was presumed this was due to shooting restrictions during the COVID-19 pandemic that made it impossible to film crossovers between the various Arrowverse series, it appears that Superman and Lois is actively ignoring the show that inspired it.
A subplot in the Superman and Lois season 2 episode "The Ties That Bind" found Lois Lane (Elizabeth Tulloch) in conflict with her business partner at the Smallville Gazette, Chrissy Beppo (Sofia Hasmik), after Lois was accused of coercing her sources on an expose into a self-help guru whom Lois had painted as a dangerous cult leader. Lois Lane defended her story and her sources, but admitted to Chrissy that the mystery source whom she quoted in the article was her younger sister, Lucy Lane. Lois' description of a woman who lost her savings and nearly died following a questionable spiritual advisor painted a radically different portrait of Lucy Lane than that presented during Supergirl season 1.
Major Lucy Lane (Jenna Dewan) was one of the prime antagonists of both Supergirl and Kara Danvers. A career military woman who followed in the footsteps of her father, Lucy attended the US Military Academy at West Point before going on to earn multiple law degrees at Harvard. Hired on at CatCo Worldwide Media as a legal consultant, Lucy quickly became a romantic rival to Kara Danvers, as both women pursued James "Jimmy" Olsen. Later, as the legal attaché to her father's staff, Lucy caused continual trouble for Supergirl and the DEO, even before she was appointed to oversee the agency after Martian Manhunter's secret identity was exposed. Despite Jenna Dewan returning to the role of Lucy Lane after a five-year absence from the Arrowverse, it is hard to reconcile the no-nonsense Lucy Lane of Supergirl season 1 with Lois Lane's description of her sister in Superman and Lois season 2.
Logically, there is no reason why Superman and Lois could not present a new version of Lucy Lane. The series has already redefined several characters who had previously appeared on Supergirl, with corrupt billionaire Morgan Edge being recast and reworked into an alter ego of the Kryptonian conqueror Tal-Rho. The show also changed the character of General Sam Lane, who was played by Glenn Morshower in Supergirl season 1 as an immoral bully who saw all aliens and superheroes as a threat to law and order. This was true to the character's portrayal in the comics, making it all the more jarring for Arrowverse fans when Superman and Lois introduced a new General Sam Lane. This General Lane, played by Dylan Walsh, was not only aware that his son-in-law was Superman, but was generally supportive of his desire to avoid being tied to any one organization.
It makes sense that Superman and Lois would not try to fully explain Supergirl's retconned history following Crisis on Infinite Earths, which merged the Earth-38 reality into the new Earth-Prime. Superman and Lois season 1 had its own history to establish, with Lois and Clark marrying earlier than they had in the original Earth-38 timeline and being the parents of twin teenage boys rather than a single infant son. Nevertheless, Superman and Lois has seemingly gone out of its way to avoid referencing anything that connected it to Supergirl and the series' treatment of Lucy Lane is only the latest example of this. While the show does not need to make continual reference to why Kara Zor-El never seems to visit the Kent farm, it would have been easy enough for General Lane to make a vague reference to a difficult past with Supergirl and the DEO to explain why he exclusively calls on Clark when the Department of Defense needs a superheroic savior.