I found the strategy for both the player and Lyin' Lauren to win! (Still requires a bit of luck)
- Call out Lauren for her lie, she will give you a rough estimate. Lie yourself when saying your dice, she will believe it. Choose the median of her estimate with your dice result to make your win almost guaranteed! (If 4 or higher, add your number by 5. If 3 or lower, add your number by 2)
- Believe her lie and tell her the truth with your result. She will be guaranteed a win
- Call out Lauren for her lie for her estimate but tell her the truth of your result so that she knows the answer. Now you have to figure out the answer with her estimate. It's a 1/3 chance you win (If she gives a single answer. Do not trust it, treat that as the estimate)
Once you win. She leaves with her earnings and you still continue on with the next opponent
This game is amazing!