Your lamb has exposed the horn core, which is extremely sensitive. As an emergency if it keeps on bleeding you can wrap clean cobwebs around the stump, otherwise as above. Over time, the stump will be covered by horn, although will never match the other side.
This is very different to when the whole horn has been torn out, core and all, when you have an emergency and need to pinch the artery between finger and thumb for a good 5 mins, then get the sheep to the vet for further treatment. They won't always survive this unless you are quick with spotting it, unlike a torn off horn sheath which is uncomfortable but survivable.