Warning: SPOILERS for Superman and Lois season 1, episode 12, "Through The Valley Of Death."
John Diggle's cameo in Superman and Lois episode 12 seems to have opened up a major plot hole regarding the finale of Arrow and the career path of his wife, Lyla Michaels. When Arrow came to an end, Lyla was said to have accepted a promotion that required her and her family to move to Metropolis, suggesting she had accepted a position higher up in the Department of Defense than Director of ARGUS. However, Diggle's most recent cameos implied that Lyla was still in charge at ARGUS and that they were still in Star City.
The Superman and Lois episode "Through The Valley Of Death" made no reference to any of any of John Diggle's earlier cameos throughout the Arrowverse this year or to the migraine headaches he had begun experiencing. Diggle's brief appearance was spent delivering a piece of specialty ammunition from ARGUS to General Sam Lane in Smallville, so that John Henry Irons could build an anti-Kryptonian weapon. Diggle was not pleased when he learned why he had been called out and said that Lyla Michaels never would have agreed to help General Lane if she'd known he was crafting a weapon to kill Superman. This raised the question of why General Lane would be contacting Lyla in the first place when there was no indication that she was still running ARGUS.
After serving as a special agent for several years, Lyla Michaels was appointed to the position of Director of ARGUS following Amanda Waller's death in the Arrow season 4 episode "A.W.O.L." She continued to serve in that role until the end of the series. The final episode of Arrow made reference to Lyla having accepted a promotion although it did not describe just what that promotion entailed or what department she would be working for now. There is no obvious way she could be promoted any higher at ARGUS when she was already running the organization and reporting directly to the Joint Chiefs as Director. This seems at odds with what little information has been revealed about John Diggle's life and ARGUS following the Arrow finale.
Diggle first cameoed in the Batwoman episode "Rebirth," where he introduced himself as being from Star City and in town on a contract with ARGUS, while competing in a private poker game for law enforcement personnel. Diggle later appeared in The Flash season 7 episode "P.O.W." where he delivered an entropy trap designed by Cisco Ramon (who had recently accepted a job in Star City as the new director of ARGUS' Technology and Science division) and helped Team Flash in fighting the Godspeed War. After experiencing a massive headache in the field, Diggle left Central City and his friends behind, saying only that he had to deal with "something I've been putting off for far too long."
It's possible that the timeline was rewritten by Crisis on Infinite Earths so that Lyla was only recently promoted to her leadership position at ARGUS, which would explain why Superman and Lois treated her as if she were still running the organization. Diggle's continued employment at ARGUS can likewise be explained by reality being rewritten in the new timeline so that he no longer had to resign from the organization as he originally did in Arrow season 7. It's also possible that Lyla doesn't directly control ARGUS anymore but still has a good deal of influence there and that General Lane contacted her rather than going through official channels. In any case, the episode could have benefited from a little more discussion clarifying just what Diggle's position at ARGUS is now and why Lyla had to move to Metropolis when ARGUS still seems to be based in Star City.