Jimmy AKA Saul Goodman, did not lie to Walt about Jimmy having a second wife. Jimmy's second wife was indirectly mentioned in Better Call Saul S05E07, "JMM". In the scene where Jimmy and Kim Wexler (who is Jimmy's third wife as of that same episode) were applying for their marriage license, there was this dialog (emphasis mine):
Court clerk: Sir, do you have documentation of your two previous dissolutions?
Jimmy: Yeah. [Jimmy hands over the documentation.]
This dialog was probably added to address Saul Goodman's mention of his second wife in Breaking Bad. From a Jan. 2018 Screen Rant article, "One Change Vince Gilligan Would Make To Breaking Bad", where Vince Gilligan was interviewed:
Breaking Bad/Better Call Saul creator Vince Gilligan has revealed one detail from the parent show he wishes he could change in light of the prequel.
Screen Rant recently talked with Vince Gilligan, the creator of both shows, about the writing process for Better Call Saul, particularly in regard to the canon of Breaking Bad. After detailing how the Jimmy/Gus paradigm caused several blocks in the writer's room, the showrunner revealed a more obscure roadblock that he's yet to be able to get around - Saul's two failed marriages:
"I'll tell you a tricky one. Off the top of my head, there was some casual reference Saul Goodman made way back in Breaking Bad about being married twice or three times or something like that. That one has bedeviled us for sure. It was just a goofy throwaway line in an episode of Breaking Bad where Saul Goodman talked about his second wife or some such and that has bedeviled us. We're trying to figure that one out. When did he a wife? And who was the second wife? Who was his first wife? Blah blah blah. That was a tricky one."