Oiling leather is a great way to protect it from future diacoloring from moisture or grime. There are a few different products out there that can help - dyes, sealants, waxes and oils.
Older products were very effective but could be toxic and problematic for disposal. I’ve used Tandy Leather Factory “Eco-Flo” in various colors. Wear gloves though, these products are designed to stain skin. I’m also a fan of their “Super Shene” product to retain the original leather color and seal the leather (don’t let it freeze though! I killed a whole bottle by storing it in the garage one winter), it’s easy to clean up and doesn’t stain my skin. Neatsfoot oil is a must for leathers that are going to be seeing the weather.
Leather edges need different protection than the hair side (the shiny smooth side that would have been the very external layer of skin) of the leather: when I first started leather working I spent hours on one project, only to have the leather start a small tear at an edge that grew to ruin all my effort. This was nice thick 12oz. leather. I quickly learned the value of finishing edges, either by heavy burnishing (I used gum tragacanth or even spit and rubbed it until it was smooth with a piece of hardwood), Fiebing’s Edge Kote, or even latex paint.
Find a local leather craft store- they are almost always friendly and willing to advise and share their experience. They may even have sample products or open work hours and work tables where you can finish your projects in store and get advice along the way.
Sorry, sounds like an advertisement. Just sharing what I’ve found has worked for me.