Yellowbird, you catch on quickly. My husband had an aunt (may she rest in peace) who was the crazy one in the family, she didn't drink or drug but she did really crazy things. Other family members just let Mavis be Mavis, and smiled and nodded and let it all go.
I thought this was odd, but in time I learned the meaning of "acceptance", it didn't mean they condoned what she did, it just meant that they took Mavis for the person she was and learned to live with her. Over time I quite liked Mavis, eccentric or not.
I suspect it will be like this with your family member. Nobody can change her, she is who she is, but accepting that, fibs and all, is part of recovery and just letting family be family.
Your recovery and program is all about you. Her lies don't make your program any less important or wonderful.
Today, rather than debate or call people out on petty matters, I use expressions a lot such as "Oh isn't that wonderful, good for you" or "Really? How nice for you" and then move on. Try it, I'll bet you can have some fun with it without anyone even knowing.