Can you describe what kind of leather you are working with?
I do leatherwork and have dealt with this, but I might have different advice depending on what it is. For example, I have
experience primarily with thicker leather for bags, shoes, etc, and I'm not sure what kind of advice to give for leather-bound
books 
.
Typically when leather gets moldy it has to do with the humidity, although well-oiled leather will get less moldy.
If leather is old and brittle, oiling it with just about any oil can help. I make my own blend of beeswax, olive oil, and essential oil (mostly beeswax but
enough olive oil to soften it up) and use that. If you want to waterproof, that's a different technique.
For most thicker leathers, I would suggest first cleaning it with a damp cloth (not too wet, the
water can leave marks) and then giving it a few thorough coatings of oil. That
should not only bring it back to a soft, pliable state but also prevent too much future moold.