If your book is being written in Dropbox writing mode, then in a Dropbox folder on your computer, you should have a folder for this book.
In that folder, there will be manuscript documents. You can edit those documents with your updates.
If you have been writing in a document somewhere else on your computer, you should be able to copy and paste the changes from that other document, to your current manuscript documents, though you will have to edit the formatting to match what you currently have in the manuscript documents in your book's Dropbox folder.
You can then see if it worked by creating a new preview in the Leanpub author menu here:
Author > Books > Book Title > Preview or Publish > Preview
If it works, you can then publish a new version here:
Author > Books > Book Title > Preview or Publish > Publish