Tandy's Leather would sells the lacing. You may need 3x the length of the side (20" x 3 =60") possibly more depending on how small the stitch is on the quiver. Or, unlace what you have in sections and then measure the length needed. Any leather shop.
I would clean it with saddle soap, then let dry before using Montana Pitch Blend.
Montana Pitch Blend leather conditioner, available thru Kustom King (online), or maybe 3 Rivers. You can do a Google search to find it. Spread it as evenly as possible, and rub it in with your hand, sheep skin pad, or small hande towel. You should work it into the leather, then let dry before doing any more. It will darken the leather some. Once the leather absorbs the oil, it may take more, try it in a small area on the backside to see if you need more.