There are several excellent books that can provide insights into the business lifecycle. Here are some recommendations:

1. "The Lean Startup: How Today's Entrepreneurs Use Continuous Innovation to Create Radically Successful Businesses" by Eric Ries - This book focuses on the different stages of a startup's lifecycle and provides valuable advice on how to navigate through them.

2. "Crossing the Chasm: Marketing and Selling High-Tech Products to Mainstream Consumers" by Geoffrey A. Moore - This book specifically focuses on the technology industry and discusses the different stages of a technology product's lifecycle, including how to bridge the gap between early adopters and mainstream customers.

3. "Built to Last: Successful Habits of Visionary Companies" by Jim Collins and Jerry I. Porras - This book examines companies that have stood the test of time and explores their different lifecycle stages, providing valuable lessons on building and sustaining a successful business.

4. "The Innovator's Dilemma: When New Technologies Cause Great Firms to Fail" by Clayton M. Christensen - This book delves into the challenges faced by established companies when disruptive technologies emerge, highlighting the importance of understanding and adapting to the different stages of the business lifecycle.

5. "The Startup Owner's Manual: The Step-By-Step Guide for Building a Great Company" by Steve Blank and Bob Dorf - This comprehensive guide provides practical advice and methodologies for every stage of a startup's lifecycle, from customer discovery to scaling.

Ultimately, the best book for learning about the business lifecycle may vary depending on your specific needs and industry. It's recommended to explore multiple resources and find the ones that resonate most with your goals and circumstances.