Did you dip the cords in 10% Iodine at birth? An infection via the umbilicus can kill a lamb, so if that is the problem she may well need an antibiotic injection from the vet, quickly.
Ah, on rereading I see they were orphan lambs so you will not know what the original treatment was. Assume the umbilicus was not treated and get it seen by the vet.
Have you sniffed her body - both near the umbilicus and over her fleece? The sense of smell is an important part in diagnosis and will help you home in on the source of infection.
An unusual smell could be indicative of a metabolic disorder which is for the vet to deal with.
Is she scouring ie diarrhoea?
Is the muck on her coat dry? If so you can brush her with a wire pin brush to get it off, if it's wet then there is something else wrong, rather than it being dried on afterbirth which the ewe has not cleaned. If it was a difficult birth, or of the ewe died, then the lamb could have been covered in bright yellow, faecal-stained birth fluids which could now be smelling. I see no problem in cleaning the lamb, as long as you dry her properly and make sure she does not lose body heat.
A photo would be helpful but a quick phone call to the vet about the umbilicus would be much better than hanging around for a possible answer here - you could take the lamb down to the surgery to save a call-out fee and let the vet see the lamb now.
It could be not much, but equally baby lambs die very quickly, so don't waste time wondering.