Diesel, many people choose not to line their bible covers, but many others want a nice finished look. IMO you have several options and I am assuming you are using veg tanned leather on the outside. A nice cloth could be glued to the inside of the cover but you then have a different edging process to contend with. You could also use a very light weight (1-2 oz) cow, calfskin or pigskin liner. These will flex nicely and while there may be some wrinkles right at the fold, the book will cover it anyway.
Personally, I'd use calf skin. I really love the feel of it. Good luck, post pics, and welcome to the forum!
Mike