This year I had a new problem with a lamb that was/is similar but different to this. Apparently it is not uncommon, so I put it on here should others encounter it and be puzzled.
A twin, she was tiny at birth and I wasn't convinced she was suckling, so gave her a number of top ups from a bottle. As she drank, I could hear a chesty rattle every time she breathed. I would withdraw the teat, wait a bit for the rattle to subside and then continue until the next rattle. The vet explained that it was the result of An abnormal connection between trachea and oesophagus that allows milk to pass into the lungs. Strangely, it did not produce a coughing reflex. Anyway, the vet said some grow through it, , and some don't and die. Well so far, at six weeks old, she is thriving, same size as her brother and just as lively. So fingers crossed.