ideal image size for book

bartonlew  wrote The images are of old documents and they will likely be reproduced in a book that is 8 1/2" x 11", so the images should be approximately that size but somewhat smaller to allow for captions.  How do I figure out what dimensions to give my photos during export to maximize their clarity and quality overall for this purpose?

Start by determining the printing requirements. For that you'll need to find out about the printer that will be used for the book. Some might require 200 pixels per inch, others 240, 300, or 360 pixels per inch, so confirm with the printing service instead of guessing.

Once you know that, you know what to enter into the Export dialog box in Lightroom. For example, if you find out that images should be 300 ppi, then in the Export dialog box in Lightroom you'll use the Image Sizing section to specify that images be Width and Height be 8.5 inches by 11 inches at 300 pixels per inch.

You may have to run a test or two, maybe even involving ordering a test book, to figure out the best sharpening settings and tone/color correction for the specific printer, paper, and ink being used.