Hi Yvonne. One of the common causes of coughing in sheep is worms. Were your lambs wormed immediately before they came to you? If not it would be a good iduea to get them wormed. Your vet is a good person to discuss a worming plan with, as he/she will know the local problems ie what you are likely to encounter and will give advice accordingly. In fact they will help you work out a whole health plan. That way you will start off on the right foot.
Your coughing lamb could just have some hay caught in its throat, if worms are not a probability.
I'm sure others will have some more suggestions.
Congratulations on getting your new sheep