I'm really intrigued by this book from Angel City Press called To Live and Dine in L.A.: Menus and the Making of the Modern City. The book is by Josh Kun and it's a collaboration between the Los Angeles Public Library and the Library Foundation of Los Angeles to remember old restaurants that have come and gone in LA's history. We often think of LA as a city of entertainment, pleasure, cars, and beaches, but it's also a city filled with a rich history of food and culinary endeavors. This book aims to recall some of that and bring it to the limelight.
The Library Foundation of Los Angeles has a great minisite surrounding this book and there's a Tumblr associated with the book as well. Both are incredibly fascinating -- especially the photos.
If you want to explore the LAPL's collection of menu's on your own, you can do so online! A large portion of their menu collection has been digitized.
Old Los Angeles Restaurants is another great site if you want to read more about LA restaurants that are no more.