That's not just an ordinary piece of lead that was flattened into a patch (or whatever). It is definitely a 3-groove Minie-ball. Look closely at its edges, near the bottom. You'll see the zig-zags from the grooves. If you hammered a Minie-ball flat, it would be about the same size as your item (indicated by the ruler you thoughtfully included in the photo). I've got a very similar one (but without the tiny holes) in my collection of dug civil war bullets.
The very small size of the holes suggest they were made for sewing it onto something, perhaps as an ID-badge. Have you examined both sides extra-closely, for any markings?