Coughing can be caused by dusty pens, dusty feed, or infectious agents. If the lamb only coughs at feeding time, dusty feed is the problem. You can dampen the feed by adding a tiny bit of water or molasses. If the lamb only coughs after running and jumping, the dust in the pen is probably the problem. You can sprinkle down the pen in late afternoon. If the lamb is coughing throughout the day, then infectious agents may be the cause.
If there is more than a month before sale time, give an injection of a long acting tetracycline (LA 200) every other day, over a 6 day period (3 times). Use a dosage of 10 mg/lb. 100 lbs = 4.5 cc or 75 lb lamb 2cc.
If the coughing continues, the infectious agent is a virus and there is no good treatment. Do try to keep the dust down, so that the coughing is not made worse by irritants in the air.
Coughing itself is rarely a big problem. However coughing, together with diet and other stressors such as coccidia, can cause rectal prolapses.